Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2
Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 213-342.

We construct a representation of the affine W-algebra of 𝔤𝔩r on the equivariant homology space of the moduli space of U r -instantons, and we identify the corresponding module. As a corollary, we give a proof of a version of the AGT conjecture concerning pure N=2 gauge theory for the group SU(r).

Our approach uses a deformation of the universal enveloping algebra of W 1+∞, which acts on the above homology space and which specializes to W(𝔤𝔩r) for all r. This deformation is constructed from a limit, as n tends to ∞, of the spherical degenerate double affine Hecke algebra of GL n .

DOI : 10.1007/s10240-013-0052-3
Schiffmann, O. 1 ; Vasserot, E. 2

1 Département de Mathématiques, Université de Paris-Sud Bâtiment 425, 91405, Orsay Cedex France
2 Département de Mathématiques, Université de Paris 7 175 rue du Chevaleret, 75013, Paris France
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Schiffmann, O.; Vasserot, E. Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A
2. Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 213-342. doi : 10.1007/s10240-013-0052-3. http://www.numdam.org/articles/10.1007/s10240-013-0052-3/

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  • Gordon, Iain; Leclerc, Bernard; Varagnolo, Michela Enveloping algebras and geometric representation theory. Abstracts from the workshop held October 31 – November 6, 2021 (hybrid meeting), Oberwolfach Rep. 18, No. 4, 2827-2891, 2021 | DOI:10.4171/owr/2021/52 | Zbl:1506.00076
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  • Rapčák, Miroslav; Soibelman, Yan; Yang, Yaping; Zhao, Gufang Cohomological Hall algebras, vertex algebras and instantons, Communications in Mathematical Physics, Volume 376 (2020) no. 3, pp. 1803-1873 | DOI:10.1007/s00220-019-03575-5 | Zbl:1508.81977
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  • Rapčák, Miroslav On extensions of gl(m|n)^ Kac-Moody algebras and Calabi-Yau singularities, Journal of High Energy Physics, Volume 2020 (2020) no. 1, p. 35 (Id/No 42) | DOI:10.1007/jhep01(2020)042 | Zbl:1434.81045
  • Harada, Koichi; Ho, Pei-Ming; Matsuo, Yutaka; Watanabe, Akimi Dimensional oxidization on coset space, Journal of High Energy Physics, Volume 2020 (2020) no. 10 | DOI:10.1007/jhep10(2020)198
  • Li, Wei; Yamazaki, Masahito Quiver Yangian from crystal melting, Journal of High Energy Physics, Volume 2020 (2020) no. 11, p. 126 (Id/No 35) | DOI:10.1007/jhep11(2020)035 | Zbl:1456.81216
  • Watanabe, Akimi; Zhu, Rui-Dong Testing Macdonald index as a refined character of chiral algebra, Journal of High Energy Physics, Volume 2020 (2020) no. 2, p. 49 (Id/No 4) | DOI:10.1007/jhep02(2020)004 | Zbl:1435.81223
  • Bourgine, Jean-Emile; Jeong, Saebyeok Journal of High Energy Physics, 2020 (2020) no. 5, p. 52 (Id/No 127) | DOI:10.1007/jhep05(2020)127 | Zbl:1437.81055
  • Procházka, Tomáš On even spin W, Journal of High Energy Physics, Volume 2020 (2020) no. 6, p. 35 (Id/No 57) | DOI:10.1007/jhep06(2020)057 | Zbl:1437.81102
  • Li, Wei Gluing affine Yangians with bi-fundamentals, Journal of High Energy Physics, Volume 2020 (2020) no. 6 | DOI:10.1007/jhep06(2020)182
  • Eberhardt, Lorenz; Procházka, Tomáš The Grassmannian VOA, Journal of High Energy Physics, Volume 2020 (2020) no. 9, p. 86 (Id/No 150) | DOI:10.1007/jhep09(2020)150 | Zbl:1454.81185
  • Feigin, Boris; Gukov, Sergei VOA [M4], Journal of Mathematical Physics, Volume 61 (2020) no. 1, p. 012302 | DOI:10.1063/1.5100059 | Zbl:1478.17025
  • Cooper, Benjamin; Samuelson, Peter The Hall algebras of surfaces. I, Journal of the Institute of Mathematics of Jussieu, Volume 19 (2020) no. 3, pp. 971-1028 | DOI:10.1017/s1474748018000324 | Zbl:1440.53098
  • Foda, Omar; Macleod, Nicholas; Manabe, Masahide; Welsh, Trevor sl^(n)N WZW conformal blocks from SU(N) instanton partition functions on C2/ZN, Nuclear Physics. B, Volume 956 (2020), p. 48 (Id/No 115038) | DOI:10.1016/j.nuclphysb.2020.115038 | Zbl:1473.81111
  • Koroteev, Peter On quiver W-algebras and defects from gauge origami, Physics Letters. B, Volume 800 (2020), p. 6 (Id/No 135101) | DOI:10.1016/j.physletb.2019.135101 | Zbl:1434.81044
  • Minets, Alexandre Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces, Selecta Mathematica. New Series, Volume 26 (2020) no. 2, p. 67 (Id/No 30) | DOI:10.1007/s00029-020-00553-x | Zbl:1444.14079
  • Arakawa, Tomoyuki; Creutzig, Thomas; Linshaw, Andrew R. W-algebras as coset vertex algebras, Inventiones Mathematicae, Volume 218 (2019) no. 1, pp. 145-195 | DOI:10.1007/s00222-019-00884-3 | Zbl:1459.17045
  • Gaiotto, Davide; Rapčák, Miroslav Vertex algebras at the corner, Journal of High Energy Physics, Volume 2019 (2019) no. 1, p. 88 (Id/No 160) | DOI:10.1007/jhep01(2019)160 | Zbl:1409.81148
  • Li, Wei; Longhi, Pietro Gluing two affine Yangians of gl1, Journal of High Energy Physics, Volume 2019 (2019) no. 10, p. 81 (Id/No 131) | DOI:10.1007/jhep10(2019)131 | Zbl:1427.83108
  • Procházka, Tomáš Instanton R-matrix and W-symmetry, Journal of High Energy Physics, Volume 2019 (2019) no. 12, p. 58 (Id/No 99) | DOI:10.1007/jhep12(2019)099 | Zbl:1431.81126
  • Eberhardt, Lorenz; Procházka, Tomáš The matrix-extended W1+ algebra, Journal of High Energy Physics, Volume 2019 (2019) no. 12, p. 35 (Id/No 175) | DOI:10.1007/jhep12(2019)175 | Zbl:1431.81124
  • Harada, Koichi; Matsuo, Yutaka Plane partition realization of (web of) W-algebra minimal models, Journal of High Energy Physics, Volume 2019 (2019) no. 2, p. 36 (Id/No 50) | DOI:10.1007/jhep02(2019)050 | Zbl:1411.81209
  • Procházka, Tomáš; Rapčák, Miroslav W-algebra modules, free fields, and Gukov-Witten defects, Journal of High Energy Physics, Volume 2019 (2019) no. 5, p. 72 (Id/No 159) | DOI:10.1007/jhep05(2019)159 | Zbl:1416.81195
  • Ahn, Changhyun; Peng, Cheng Chiral algebras of two-dimensional SYK models, Journal of High Energy Physics, Volume 2019 (2019) no. 7, p. 26 (Id/No 92) | DOI:10.1007/jhep07(2019)092 | Zbl:1418.81083
  • Bershtein, Mikhail; Tsymbaliuk, Alexander Homomorphisms between different quantum toroidal and affine Yangian algebras, Journal of Pure and Applied Algebra, Volume 223 (2019) no. 2, pp. 867-899 | DOI:10.1016/j.jpaa.2018.05.003 | Zbl:1460.17019
  • Galakhov, Dmitry BPS Hall algebra of scattering Hall states, Nuclear Physics. B, Volume 946 (2019), p. 33 (Id/No 114693) | DOI:10.1016/j.nuclphysb.2019.114693 | Zbl:1430.81078
  • Bourgine, J.-E.; Zhang, Kilar Physics Letters. B, 789 (2019), pp. 610-619 | DOI:10.1016/j.physletb.2018.11.066 | Zbl:1406.81058
  • Negut, Andrei Shuffle algebras associated to surfaces, Selecta Mathematica. New Series, Volume 25 (2019) no. 3, p. 57 (Id/No 36) | DOI:10.1007/s00029-019-0481-z | Zbl:1427.14023
  • Guay, Nicolas; Nakajima, Hiraku; Wendlandt, Curtis Coproduct for Yangians of affine Kac-Moody algebras, Advances in Mathematics, Volume 338 (2018), pp. 865-911 | DOI:10.1016/j.aim.2018.09.013 | Zbl:1447.17012
  • Nekrasov, Nikita; Pestun, Vasily; Shatashvili, Samson Quantum geometry and quiver gauge theories, Communications in Mathematical Physics, Volume 357 (2018) no. 2, pp. 519-567 | DOI:10.1007/s00220-017-3071-y | Zbl:1393.81033
  • Neguţ, Andrei The q-AGT-W relations via shuffle algebras, Communications in Mathematical Physics, Volume 358 (2018) no. 1, pp. 101-170 | DOI:10.1007/s00220-018-3102-3 | Zbl:1407.16029
  • Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng Twin-plane-partitions and N=2 affine Yangian, Journal of High Energy Physics, Volume 2018 (2018) no. 11, p. 62 (Id/No 192) | DOI:10.1007/jhep11(2018)192 | Zbl:1405.81053
  • Procházka, Tomáš; Rapčák, Miroslav Webs of W-algebras, Journal of High Energy Physics, Volume 2018 (2018) no. 11, p. 89 (Id/No 109) | DOI:10.1007/jhep11(2018)109 | Zbl:1404.81263
  • Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng; Zhang, Hong The supersymmetric affine Yangian, Journal of High Energy Physics, Volume 2018 (2018) no. 5, p. 32 (Id/No 200) | DOI:10.1007/jhep05(2018)200 | Zbl:1391.81161
  • Bourgine, Jean-Emile; Fioravanti, Davide Seiberg-Witten period relations in Omega background, Journal of High Energy Physics, Volume 2018 (2018) no. 8, p. 22 (Id/No 124) | DOI:10.1007/jhep08(2018)124 | Zbl:1396.81193
  • Bourgine, Jean-Emile; Fioravanti, Davide Quantum integrability of N=2 4d gauge theories, Journal of High Energy Physics, Volume 2018 (2018) no. 8, p. 25 (Id/No 125) | DOI:10.1007/jhep08(2018)125 | Zbl:1396.81110
  • Cautis, Sabin; Lauda, Aaron D.; Licata, Anthony M.; Sussan, Joshua W-algebras from Heisenberg categories, Journal of the Institute of Mathematics of Jussieu, Volume 17 (2018) no. 5, pp. 981-1017 | DOI:10.1017/s1474748016000189 | Zbl:1405.81045
  • Koroteev, Peter; Sciarappa, Antonio Quantum hydrodynamics from large-n supersymmetric gauge theories, Letters in Mathematical Physics, Volume 108 (2018) no. 1, pp. 45-95 | DOI:10.1007/s11005-017-0996-1 | Zbl:1380.81155
  • Kimura, Taro; Pestun, Vasily Quiver W-algebras, Letters in Mathematical Physics, Volume 108 (2018) no. 6, pp. 1351-1381 | DOI:10.1007/s11005-018-1072-1 | Zbl:1388.81850
  • Bastian, Brice; Hohenegger, Stefan; Iqbal, Amer; Rey, Soo-Jong Triality in little string theories, Physical Review D, Volume 97 (2018) no. 4 | DOI:10.1103/physrevd.97.046004
  • Bourgine, Jean-Emile Webs of Quantum Algebra Representations in 5d N=1 Super Yang–Mills, Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1, Volume 263 (2018), p. 209 | DOI:10.1007/978-981-13-2715-5_11
  • Cautis, Sabin; Lauda, Aaron D.; Licata, Anthony M.; Samuelson, Peter; Sussan, Joshua The elliptic Hall algebra and the deformed Khovanov Heisenberg category, Selecta Mathematica. New Series, Volume 24 (2018) no. 5, pp. 4041-4103 | DOI:10.1007/s00029-018-0429-8 | Zbl:1402.81172
  • Kodera, Ryosuke; Nakajima, Hiraku Quantized Coulomb brances of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras, String-Math 2016. Proceedings of the conference, Collège de France, Paris, France, June 27 – July 2, 2016, Providence, RI: American Mathematical Society (AMS); Boston, MA: International Press, 2018, pp. 49-78 | DOI:10.1090/pspum/098/01720 | Zbl:1469.20006
  • Tsymbaliuk, Alexander The affine Yangian of gl1 revisited, Advances in Mathematics, Volume 304 (2017), pp. 583-645 | DOI:10.1016/j.aim.2016.08.041 | Zbl:1350.81017
  • Ren, Jie; Soibelman, Yan Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for 2-dimensional Calabi-Yau categories (with an appendix by Ben Davison), Algebra, geometry, and physics in the 21st century. Kontsevich Festschrift, Basel: Birkhäuser/Springer, 2017, pp. 261-293 | DOI:10.1007/978-3-319-59939-7_7 | Zbl:1385.16012
  • Oğuz, Can Ozan; Reeks, Michael Trace of the twisted Heisenberg category, Communications in Mathematical Physics, Volume 356 (2017) no. 3, pp. 1117-1154 | DOI:10.1007/s00220-017-2992-9 | Zbl:1388.18009
  • Shan, P.; Varagnolo, M.; Vasserot, E. On the center of quiver Hecke algebras, Duke Mathematical Journal, Volume 166 (2017) no. 6 | DOI:10.1215/00127094-3792705
  • Bourgine, J.-E.; Fukuda, M.; Harada, K.; Matsuo, Y.; Zhu, R.-D. (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters, Journal of High Energy Physics, Volume 2017 (2017) no. 11, p. 51 (Id/No 34) | DOI:10.1007/jhep11(2017)034 | Zbl:1383.83156
  • Bourgine, J.-E.; Fukuda, M.; Matsuo, Y.; Zhu, R.-D. Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver, Journal of High Energy Physics, Volume 2017 (2017) no. 12, p. 27 (Id/No 15) | DOI:10.1007/jhep12(2017)015 | Zbl:1383.81265
  • Gaberdiel, Matthias R.; Gopakumar, Rajesh; Li, Wei; Peng, Cheng Higher spins and Yangian symmetries, Journal of High Energy Physics, Volume 2017 (2017) no. 4, p. 29 (Id/No 152) | DOI:10.1007/jhep04(2017)152 | Zbl:1378.81116
  • Carlsson, Erik AGT and the Segal-Sugawara construction, Journal of Mathematical Physics, Volume 58 (2017) no. 1, p. 011703 | DOI:10.1063/1.4974352 | Zbl:1355.81107
  • Tachikawa, Yuji A brief review of the 2d/4d correspondences, Journal of Physics A: Mathematical and Theoretical, Volume 50 (2017) no. 44, p. 37 (Id/No 443012) | DOI:10.1088/1751-8121/aa5df8 | Zbl:1377.81110
  • Bartocci, Claudio; Bruzzo, Ugo; Lanza, Valeriano; Rava, Claudio L. S. Hilbert schemes of points of OP1(n) as quiver varieties, Journal of Pure and Applied Algebra, Volume 221 (2017) no. 8, pp. 2132-2155 | DOI:10.1016/j.jpaa.2016.12.012 | Zbl:1400.14031
  • Rim, Chaiho; Zhang, Hong Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation, Nuclear Physics. B, Volume 919 (2017), pp. 182-208 | DOI:10.1016/j.nuclphysb.2017.03.012 | Zbl:1361.81098
  • Fukuda, M.; Harada, K.; Matsuo, Y.; Zhu, R.-D. The Maulik–Okounkov R-matrix from the Ding–Iohara–Miki algebra, Progress of Theoretical and Experimental Physics, Volume 2017 (2017) no. 9 | DOI:10.1093/ptep/ptx123
  • Bruzzo, Ugo; Pedrini, Mattia; Sala, Francesco; Szabo, Richard J. Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces, Advances in Mathematics, Volume 288 (2016), pp. 1175-1308 | DOI:10.1016/j.aim.2015.11.005 | Zbl:1375.81223
  • Schiffmann, Olivier Indecomposable vector bundles and stable Higgs bundles over smooth projective curves, Annals of Mathematics. Second Series, Volume 183 (2016) no. 1, pp. 297-362 | DOI:10.4007/annals.2016.183.1.6 | Zbl:1342.14076
  • Soibelman, Yan Remarks on cohomological Hall algebras and their representations, Arbeitstagung Bonn 2013. In memory of Friedrich Hirzebruch. Proceedings of the meeting, Bonn, Germany, May, 22–28, 2013, Basel: Birkhäuser/Springer, 2016, pp. 355-385 | DOI:10.1007/978-3-319-43648-7_13 | Zbl:1378.11068
  • Davison, Ben Cohomological Hall algebras and character varieties, International Journal of Mathematics, Volume 27 (2016) no. 07, p. 1640003 | DOI:10.1142/s0129167x16400036
  • Pedrini, Mattia; Sala, Francesco; Szabo, Richard J. AGT relations for abelian quiver gauge theories on ALE spaces, Journal of Geometry and Physics, Volume 103 (2016), pp. 43-89 | DOI:10.1016/j.geomphys.2016.01.004 | Zbl:1332.14022
  • Szabo, Richard J. Journal of Geometry and Physics, 109 (2016), pp. 83-121 | DOI:10.1016/j.geomphys.2015.09.005 | Zbl:1348.81328
  • Procházka, Tomáš W -symmetry, topological vertex and affine Yangian, Journal of High Energy Physics, Volume 2016 (2016) no. 10, p. 73 (Id/No 77) | DOI:10.1007/jhep10(2016)077 | Zbl:1390.81252
  • Awata, Hidetoshi; Kanno, Hiroaki; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations, Journal of High Energy Physics, Volume 2016 (2016) no. 10, p. 49 (Id/No 47) | DOI:10.1007/jhep10(2016)047 | Zbl:1390.81221
  • Bourgine, Jean-Emile; Matsuo, Yutaka; Zhang, Hong Holomorphic field realization of SH c and quantum geometry of quiver gauge theories, Journal of High Energy Physics, Volume 2016 (2016) no. 4, p. 1 | DOI:10.1007/jhep04(2016)167
  • Awata, Hidetoshi; Kanno, Hiroaki; Matsumoto, Takuya; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor Explicit examples of DIM constraints for network matrix models, Journal of High Energy Physics, Volume 2016 (2016) no. 7, p. 67 (Id/No 103) | DOI:10.1007/jhep07(2016)103 | Zbl:1390.81206
  • Bershtein, Mikhail; Feigin, Boris; Litvinov, Alexei Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations, Letters in Mathematical Physics, Volume 106 (2016) no. 1, pp. 29-56 | DOI:10.1007/s11005-015-0802-x | Zbl:1395.17058
  • Neguţ, Andrei Exts and the AGT relations, Letters in Mathematical Physics, Volume 106 (2016) no. 9, pp. 1265-1316 | DOI:10.1007/s11005-016-0865-3 | Zbl:1348.14030
  • Yanagida, Shintarou A note on Bridgeland's Hall algebra of two-periodic complexes, Mathematische Zeitschrift, Volume 282 (2016) no. 3-4, pp. 973-991 | DOI:10.1007/s00209-015-1573-x | Zbl:1403.16011
  • Teschner, Jörg Exact Results on N=2 Supersymmetric Gauge Theories, New Dualities of Supersymmetric Gauge Theories (2016), p. 1 | DOI:10.1007/978-3-319-18769-3_1
  • Tachikawa, Yuji A review on instanton counting and W-algebras, New dualities of supersymmetric gauge theories, Cham: Springer, 2016, pp. 79-120 | DOI:10.1007/978-3-319-18769-3_4 | Zbl:1334.81073
  • Bourgine, Jean-Emile; Fioravanti, Davide Mayer expansion of the Nekrasov prepotential: the subleading ϵ2-order, Nuclear Physics. B, Volume 906 (2016), pp. 408-440 | DOI:10.1016/j.nuclphysb.2016.03.017 | Zbl:1334.81065
  • Mironov, A.; Morozov, A.; Zenkevich, Y. Ding–Iohara–Miki symmetry of network matrix models, Physics Letters B, Volume 762 (2016), p. 196 | DOI:10.1016/j.physletb.2016.09.033
  • Bourgine, J.-E.; Fukuda, M.; Matsuo, Y.; Zhang, H.; Zhu, R.-D. Coherent states in quantum W1+ algebra and qq-character for 5d super Yang–Mills, Progress of Theoretical and Experimental Physics, Volume 2016 (2016) no. 12, p. 123B05 | DOI:10.1093/ptep/ptw165
  • Cherednik, Ivan DAHA-Jones polynomials of torus knots, Selecta Mathematica. New Series, Volume 22 (2016) no. 2, pp. 1013-1053 | DOI:10.1007/s00029-015-0210-1 | Zbl:1360.14076
  • Bourgine, Jean-Emile Spherical Hecke algebra in the Nekrasov-Shatashvili limit, Journal of High Energy Physics, Volume 2015 (2015) no. 1, p. 36 (Id/No 114) | DOI:10.1007/jhep01(2015)114 | Zbl:1388.81293
  • Belavin, Vladimir; Foda, Omar; Santachiara, Raoul AGT, N-Burge partitions and WN minimal models, Journal of High Energy Physics, Volume 2015 (2015) no. 10, p. 38 (Id/No 73) | DOI:10.1007/jhep10(2015)073 | Zbl:1388.81633
  • Fukuda, M.; Nakamura, S.; Matsuo, Y.; Zhu, R.-D. SH c realization of minimal model CFT: triality, poset and Burge condition, Journal of High Energy Physics, Volume 2015 (2015) no. 11 | DOI:10.1007/jhep11(2015)168
  • Nazarov, Maxim; Sklyanin, Evgeny Lax operator for Macdonald symmetric functions, Letters in Mathematical Physics, Volume 105 (2015) no. 7, pp. 901-916 | DOI:10.1007/s11005-015-0770-1 | Zbl:1316.05123
  • Bourgine, Jean-Emile; Fioravanti, Davide Physics Letters. B, 750 (2015), pp. 139-146 | DOI:10.1016/j.physletb.2015.09.002 | Zbl:1364.81219
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  • Nakamura, Satoshi; Okazawa, Futoshi; Matsuo, Yutaka Recursive method for the Nekrasov partition function for classical Lie groups, Progress of Theoretical and Experimental Physics, Volume 2015 (2015) no. 3 | DOI:10.1093/ptep/ptv014
  • Nakamura, Satoshi On the Jeffrey–Kirwan residue ofBCD-instantons, Progress of Theoretical and Experimental Physics, Volume 2015 (2015) no. 7, p. 073B02 | DOI:10.1093/ptep/ptv085
  • Zhu, Rui-Dong; Matsuo, Yutaka Yangian associated with 2D𝒩= 1 SCFT, Progress of Theoretical and Experimental Physics, Volume 2015 (2015) no. 9, p. 093A01 | DOI:10.1093/ptep/ptv116
  • Bourgine, Jean-Emile Confinement and Mayer cluster expansions, International Journal of Modern Physics A, Volume 29 (2014) no. 15, p. 32 (Id/No 1450077) | DOI:10.1142/s0217751x14500778 | Zbl:1295.82009
  • Nazarov, M. L.; Sklyanin, E. K. Sekiguchi-Debiard operators at infinity, Communications in Mathematical Physics, Volume 324 (2013) no. 3, pp. 831-849 | DOI:10.1007/s00220-013-1821-z | Zbl:1408.81016
  • Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Yagi, Futoshi N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae, Journal of High Energy Physics, Volume 2013 (2013) no. 1, p. 30 (Id/No 014) | DOI:10.1007/jhep01(2013)014 | Zbl:1342.81263
  • Hama, Naofumi; Hosomichi, Kazuo AGT relation in the light asymptotic limit, Journal of High Energy Physics, Volume 2013 (2013) no. 10, p. 10 (Id/No 152) | DOI:10.1007/jhep10(2013)152 | Zbl:1342.81288
  • Tan, Meng-Chwan M-theoretic derivations of 4d-2d dualities: from a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems, Journal of High Energy Physics, Volume 2013 (2013) no. 7, p. 173 (Id/No 171) | DOI:10.1007/jhep07(2013)171 | Zbl:1342.83431
  • Arbesfeld, N.; Schiffmann, O. A presentation of the deformed W1+ algebra., Symmetries, integrable systems and representations. Proceedings of the conference on infinite analysis: frontier of integrability, Tokyo, Japan, July 25–29, 2011 and the conference on symmetries, integrable systems and representations, Lyon, France, December 13–16, 2011, London: Springer, 2013, pp. 1-13 | DOI:10.1007/978-1-4471-4863-0_1 | Zbl:1310.16024
  • Kanno, Shoichi; Matsuo, Yutaka; Zhang, Hong Virasoro constraint for Nekrasov instanton partition function, Journal of High Energy Physics, Volume 2012 (2012) no. 10, p. 24 (Id/No 97) | DOI:10.1007/jhep10(2012)097 | Zbl:1397.81156
  • Bulycheva, Kseniya; Chen, Heng-yu; Gorsky, Alexander; Koroteev, Peter BPS states in omega background and integrability, Journal of High Energy Physics, Volume 2012 (2012) no. 10, p. 48 (Id/No 116) | DOI:10.1007/jhep10(2012)116 | Zbl:1397.81344
  • Yagi, Junya Compactification on the ω-background and the AGT correspondence, Journal of High Energy Physics, Volume 2012 (2012) no. 9, p. 20 (Id/No 101) | DOI:10.1007/jhep09(2012)101 | Zbl:1397.81405

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