We construct a representation of the affine W-algebra of
Our approach uses a deformation of the universal enveloping algebra of W
1+∞, which acts on the above homology space and which specializes to
@article{PMIHES_2013__118__213_0, author = {Schiffmann, O. and Vasserot, E.}, title = {Cherednik algebras, {W-algebras} and the equivariant cohomology of the moduli space of instantons on {<strong>A</strong> \protect\textsuperscript{2}}}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {213--342}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {118}, year = {2013}, doi = {10.1007/s10240-013-0052-3}, mrnumber = {3150250}, zbl = {1284.14008}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-013-0052-3/} }
TY - JOUR AU - Schiffmann, O. AU - Vasserot, E. TI - Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2 JO - Publications Mathématiques de l'IHÉS PY - 2013 SP - 213 EP - 342 VL - 118 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://www.numdam.org/articles/10.1007/s10240-013-0052-3/ DO - 10.1007/s10240-013-0052-3 LA - en ID - PMIHES_2013__118__213_0 ER -
%0 Journal Article %A Schiffmann, O. %A Vasserot, E. %T Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2 %J Publications Mathématiques de l'IHÉS %D 2013 %P 213-342 %V 118 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://www.numdam.org/articles/10.1007/s10240-013-0052-3/ %R 10.1007/s10240-013-0052-3 %G en %F PMIHES_2013__118__213_0
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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- 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
- 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
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-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 - Twin-plane-partitions and
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 - Webs of
-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 - 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
- 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
- Quantum integrability of
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 - 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
- Quantum hydrodynamics from large-
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 - 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
- Triality in little string theories, Physical Review D, Volume 97 (2018) no. 4 | DOI:10.1103/physrevd.97.046004
- Webs of Quantum Algebra Representations in 5d
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 - 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
- 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
- The affine Yangian of
revisited, Advances in Mathematics, Volume 304 (2017), pp. 583-645 | DOI:10.1016/j.aim.2016.08.041 | Zbl:1350.81017 - 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
- 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
- On the center of quiver Hecke algebras, Duke Mathematical Journal, Volume 166 (2017) no. 6 | DOI:10.1215/00127094-3792705
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-webs of DIM representations, 5d 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 - 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
- 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
- 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
- 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
- Hilbert schemes of points of
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 - 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
- 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
- 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
- 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
- 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
- Cohomological Hall algebras and character varieties, International Journal of Mathematics, Volume 27 (2016) no. 07, p. 1640003 | DOI:10.1142/s0129167x16400036
- 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
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-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 - Toric Calabi-Yau threefolds as quantum integrable systems.
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- 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
- 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
- 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
- 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
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Supersymmetric Gauge Theories, New Dualities of Supersymmetric Gauge Theories (2016), p. 1 | DOI:10.1007/978-3-319-18769-3_1 - 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
- Mayer expansion of the Nekrasov prepotential: the subleading
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- Coherent states in quantum
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 - 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
- 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
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- 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
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- Developments of theory of effective prepotential from extended Seiberg–Witten system and matrix models, Progress of Theoretical and Experimental Physics, Volume 2015 (2015) no. 11, p. 11B103 | DOI:10.1093/ptep/ptv124
- 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
- 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
- Yangian associated with 2D𝒩= 1 SCFT, Progress of Theoretical and Experimental Physics, Volume 2015 (2015) no. 9, p. 093A01 | DOI:10.1093/ptep/ptv116
- 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
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gauge theories on toric singularities, blow-up formulae and -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 - 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
- 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
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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 - 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
- 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
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