Categorification of Lie algebras [after Rouquier, Khovanov-Lauda, ...]
Séminaire Bourbaki volume 2012/2013 : exposés 1059-1073 - Avec table par noms d'auteurs de 1948/49 à 2012/13, Astérisque, no. 361 (2014), Exposé no. 1072, 23 p.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez le site de la revue.
@incollection{AST_2014__361__397_0,
     author = {Kamnitzer, Joel},
     title = {Categorification of {Lie} algebras [after {Rouquier,} {Khovanov-Lauda,} ...]},
     booktitle = {S\'eminaire Bourbaki volume 2012/2013 : expos\'es 1059-1073 - Avec table par noms d'auteurs de 1948/49 \`a 2012/13},
     series = {Ast\'erisque},
     note = {talk:1072},
     pages = {397--419},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {361},
     year = {2014},
     zbl = {1356.17008},
     language = {en},
     url = {http://www.numdam.org/item/AST_2014__361__397_0/}
}
TY  - CHAP
AU  - Kamnitzer, Joel
TI  - Categorification of Lie algebras [after Rouquier, Khovanov-Lauda, ...]
BT  - Séminaire Bourbaki volume 2012/2013 : exposés 1059-1073 - Avec table par noms d'auteurs de 1948/49 à 2012/13
AU  - Collectif
T3  - Astérisque
N1  - talk:1072
PY  - 2014
SP  - 397
EP  - 419
IS  - 361
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2014__361__397_0/
LA  - en
ID  - AST_2014__361__397_0
ER  - 
%0 Book Section
%A Kamnitzer, Joel
%T Categorification of Lie algebras [after Rouquier, Khovanov-Lauda, ...]
%B Séminaire Bourbaki volume 2012/2013 : exposés 1059-1073 - Avec table par noms d'auteurs de 1948/49 à 2012/13
%A Collectif
%S Astérisque
%Z talk:1072
%D 2014
%P 397-419
%N 361
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2014__361__397_0/
%G en
%F AST_2014__361__397_0
Kamnitzer, Joel. Categorification of Lie algebras [after Rouquier, Khovanov-Lauda, ...], dans Séminaire Bourbaki volume 2012/2013 : exposés 1059-1073 - Avec table par noms d'auteurs de 1948/49 à 2012/13, Astérisque, no. 361 (2014), Exposé no. 1072, 23 p. http://www.numdam.org/item/AST_2014__361__397_0/

[Ara] A. Arabia - "Cycles de Schubert et cohomologie equivariante de K/T", Invent. Math. 85 (1986), no. 1, p. 39-52. | DOI | EuDML | Zbl

[Ari] S. Ariki - "On the decomposition numbers of the Hecke algebra of G(m,1,n)", J. Math. Kyoto Univ. 36 (1996), no. 4, p. 789-808. | DOI | Zbl

[BFK] J. Bernstein, I. Frenkel & M. Khovanov - "A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors", Selecta Math. (N.S.) 5 (1999), no. 2, p. 199-241. | DOI | Zbl

[B] J. Brundan - "Quiver Hecke algebras and categorification", arXiv: 1301.5868. | DOI

[BK] J. Brundan & A. Kleshchev - "Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras", Invent. Math. 178 (2009), no. 3, p. 451-484. | DOI | Zbl

[C] S. Cautis - "Equivalences and stratified flops", Compos. Math. 148 (2012), no. 1, p. 185-208. | DOI | Zbl

[CKL] S. Cautis, J. Kamnitzer & A. Licata - "Derived equivalences for cotangent bundles of Grassmannians via categorical sl2 actions", J. Reine Angew. Math. 675 (2013), p. 53-99. | Zbl

[CL] S. Cautis & A. Lauda - "Implicit structure in 2-representations of quantum groups", arXiv:1111.1431. | DOI | Zbl

[CR] J. Chuang & R. Rouquier - "Derived equivalences for symmetric groups and sl2-categorification", Ann. of Math. (2) 167 (2008), no. 1, p. 245-298. | DOI | Zbl

[Gi] V. Ginzburg - "Geometric methods in the representation theory of Hecke algebras and quantum groups", in Representation theories and algebraic geometry (Montreal, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 514, Kluwer Acad. Publ., Dordrecht, 1998, p. 127-183. | DOI | Zbl

[Gr] I. Grojnowski - "Affine sl p controls the modular representation theory of the symmetric groups and related Hecke algebras", math/9907129.

[KK] S.-J. Kang & M. Kashiwara - "Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras", Invent. Math. 190 (2012), no. 3, p. 699-742. | DOI | Zbl

[Ka] M. Kashiwara - "Biadjointness in cyclotomic Khovanov-Lauda-Rouquier algebras", Publ. Res. Inst. Math. Sci. 48 (2012). no. 3, p. 501-524. | DOI | Zbl

[KL1] M. Khovanov & A. D. Lauda - "A diagrammatic approach to categorification of quantum groups. I", Represent. Theory 13 (2009), p. 309-347. | DOI | Zbl

[KL2] M. Khovanov & A. D. Lauda, "A diagrammatic approach to categorification of quantum groups II", Trans. Amer. Math. Soc. 363 (2011), no. 5, p. 2685-2700. | DOI | Zbl

[KL3] M. Khovanov & A. D. Lauda, "A categorification of quantum sl(n)". Quantum Topol. 1 (2010), no. 1, p. 1-92. | DOI | Zbl

[LLT] A. Lascoux, B. Leclerc & J.-Y. Thibon - "Hecke algebras at roots of unity and crystal bases of quantum affine algebras", Comm. Math. Phys. 181 (1996), no. 1, p. 205-263. | DOI | Zbl

[La] A. D. Lauda - "A categorification of quantum sl(2)", Adv. Math. 225 (2010), no. 6, p. 3327-3424. | Zbl

[LV] A. D. Lauda & M. Vazirani - "Crystals from categorified quantum groups", Adv. Math. 228 (2011), no. 2, p. 803-861 . | MR | Zbl

[Lu1] G. Lusztig - "Canonical bases arising from quantized enveloping algebras", J. Amer. Math. Soc. 3 (1990), no. 2, p. 447-498. | DOI | MR | Zbl

[Lu2] G. Lusztig, "Quivers, perverse sheaves, and quantized enveloping algebras", Amer. Math. Soc. 4 (1991), no. 2, p. 365-421. | DOI | MR | Zbl

[N] H. Nakajima - "Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras", Duke Math. J. 76 (1994), no. 2, p. 365-416. | MR | Zbl

[R1] R. Rouquier - "Catégories dérivées et géométrie birationnelle (d'après Bondal, Orlov, Bridgeland, Kawamata et al.)", in Séminaire Bourbaki, vol 2004/2005, Astérisque, vol. 307, Soc. Math. France, Paris, 2006, exp. n° 946, p. 283-307. | EuDML | Numdam | MR | Zbl

[R2] R. Rouquier, "2-Kac-Moody algebras", arXiv:0812.5023.

[R3] R. Rouquier, "Quiver Hecke algebras and 2-Lie algebras", Algebra Colloq. 19 (2012), no. 2, p. 359-410. | DOI | MR | Zbl

[ST] P. Seidel & R. Thomas - "Braid group actions on derived categories of coherent sheaves", Duke Math. J. 108 (2001), no. 1, p. 37-108. | DOI | MR | Zbl

[VV] M. Varagnolo & E. Vasserot - "Canonical bases and KLR-algebras", J. reine angew. Math. 659 (2011), p. 67-100. | MR | Zbl

[W1] B. Webster - "Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products", arXiv: 1001.2020.

[W2] B. Webster, "A categorical action on quantized quiver varieties", arXiv:1208.5957. | DOI

[Z] H. Zheng - "Categorification of integrable representations of quantum groups", arXiv:0803.3668 | DOI | MR | Zbl