Équations de Knizhnik-Zamolodchikov et théorie des représentations

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1. [A] H.H. Andersen - Quantum groups, invariants of 3-manifolds and semi-simple tensor categories, Preprint. 
2. [AJS] H.H. Andersen, J.C. Jantzen and W. Soergel - Representation of quantum groups at p-root of unity and of semi-simple groups in characteristic p : independence of p, Astérisque220 (1994). Zbl0802.17009MR1272539
3. [Ao1] K. Aomoto - Fonctions hyperlogarithmiques et groupes de monodromie unipotent, J. Fac. Sc. Tokyo, 25 (1978) 149-156. Zbl0416.32020MR509582
4. [Ao2] K. Aomoto - Gauss-Manin connection of integrals of different products, J. Fac. Sc. Tokyo, 39 (1987) 191-208. Zbl0619.32010MR879924
5. [BPZ] A.A. Belavin, A.N. Polyakov and A.B. Zamolodchikov - Infinite conformal symmetries in two-dimensional conformal field theory, Nucl. Phys. Zbl0661.17013
6. B, 241 (1984) 333-380. MR757857
7. [C] L. Casian - Kazhdan-Lusztig conjecture in the negative level case (Kač- Moody Lie algebras of affine type), Preprint. 
8. [D] V.G. Drinfeld - On almost cocommutative Hopf algebras, Algebra and Analysis1 (1987) 30-46. Zbl0718.16035MR1025154
9. [FSV] B.L. Feigin, V.V. Schechtman and A.N. Varchenko - On algebraic equations satisfied by correlators in the Wess-Zumino-Witten model, Letter Mat. Phys.20 (1990) 291-297. Zbl0719.35080MR1077961
10. [F] M. Finkelberg - Fusion categories, HarvardP.H.D. ( Mai 1993). 
11. [J1] M. Jimbo - Quantum R-matrix for the generalized Todda system, Comm. Math. Phys.102 (1986) 537-547. Zbl0604.58013MR824090
12. [J2] M. Jimbo: Quantum R-matrix related to the generalized Todda lattice, Lect. Notes Phys., Springer Verlag246 (1986). MR848629
13. [G] C. Gawędzki - Conformal field theory, Sém. Bourbaki, exp. n° 704, novembre 1988, Astérisque177-178 (1989), 95-126. Zbl0699.53085MR1040570
14. [GM1] G. Georgiev et O. Mathieu - Catégorie de fusion pour les groupes de Chevalley, Comptes Rendus Acad. Sc. Paris, 315 (1992) 659-662. Zbl0801.20014MR1183798
15. [GM2] G. Georgiev et O. Mathieu - Fusion category for Chevalley groups, Proceedings de la conf. Conformal field theory, Mount Holliock, Juin 1992 (À paraître). 
16. [G] P. Goddard - Meromorphic conformal field theory, Preprint. Zbl0742.17027MR1026966
17. [HL] Y.Z. Huang and J. Lepowsky - Towards a theory for tensor products for representations of a vertex operator algebra, Proc. 20th International Conference on Differential Geometry Methods in Theoritical Physics, New York1991, ed. S. Catto and A. Rocha Carridi, World Sc., Singapore, 1 (1992) 344-354. Zbl0829.17025MR1225125
18. [K] V.G. Kac - Infinite dimensional Lie algebras, Birkhaüser, Prog. Math.44 (1983). Zbl0537.17001MR739850
19. [KR] V.G. Kac and A.K. Raina - Highest weights representations of infinite di- mensional Lie algebras, World Sc., Singapore. Adv. Ser. Math. Phys.2 (1988). Zbl0668.17012
20. [KL1] D. Kazhdan G. Lusztig - Affine Lie algebras and quantum groups, Int. Math. Research Notices, Duke Math. J.62 (1991) 21-29. Zbl0726.17015MR1104840
21. [KL2] D. Kazhdan G. Lusztig - Tensor structures arising from affine Lie algebras (Preprint en 5 parties). 
22. [KnZ] V.G. Knizhnik and A.B. Zamolodchikov - Current algebras and Wess-Zumino model in two dimensions, Nucl. Phys.B247 (1984) 83-103. Zbl0661.17020MR853258
23. [K1] T. Kohno - Hecke algebra representations of braid groups and classical Yang-Baxter equations. Comtemp. Math78 (1988) 339-363. Zbl0661.20026MR975088
24. [K2] T. Kohno - Monodromy representations of braid groups and classical Yang-Baxter equations, Ann. Ins. Fourrier37 (1987) 139-160. Zbl0634.58040MR927394
25. [L1] G. Lusztig - Some problems in the representation theory of finite groups, Proc. Symp. Pure Math.36 (1980) 185-203. MR604598
26. [L2] G. Lusztig - Monodromic system on affine flag manifolds, Preprint. MR1276910
27. [MS] G. Moore and N. Seiberg - Classical and quantum conformal field theory, Comm. Math. Phys.123 (1988) 177-254. Zbl0694.53074MR1002038
28. [R] M. Rosso - Représentations irréductibles du q-analogue de l'algèbre enveloppante d'une algèbre de Lie, C.R.A.S.305 (1987) 587-590. Zbl0624.17005MR917574
29. [SV] V.V. Schechtman and A.N. Varchenko - Hypergeometric solutions of Knizhnik-Zamolodchikov equations, Letters Math. Phys.20 (1990) 279-283. Zbl0719.35079MR1077959
30. [TK] A. Tsuchiya and Y. Kanie - Vertex operators in conformal field theory on P1 and monodromy representations of braid groups, Adv. Study in Pure Math.19 (1989) 459-565. Zbl0661.17021
31. [TUY] A. Tsuchiya, K. Ueno and Y. Yamada - Conformal field theory on universal family of stable curve with gauges symmetries, Adv. Studies in Pures Math.19 (1989) 459-565. Zbl0696.17010MR1048605
32. [V] E. Verlinde - Fusion rules and modular transformations in 2D-conformal field theory, Nucl. Phys.B300 (1988) 360-375. Zbl1180.81120MR954762
33. [W] E. Witten - Quantum field theory, Grassmannians and algebraic curves, Comm. Math. Phys.113 (1987) 529 Zbl0636.22012MR923632

1. Wolfgang Soergel, Conjectures de Lusztig