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On quantum groups. (English) Zbl 0698.16007

A Hecke algebra is associated in a natural way to every quantum group of Drinfeld and Jimbo. Then a conjecture is formulated which relates the representation theory of a quantum group at a fixed root of 1 to the representation theory of an affine Lie algebra at a fixed negative level.

MSC:

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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References:

[1] Casian, L., Proof of the Kazhdan-Lusztig conjecture for Kac-Moody algebras (1989), (Symmetrizable case), preprint
[2] Drinfeld, V. G., Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl., 32, 254-258 (1985) · Zbl 0588.17015
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[10] Moore, G.; Seiberg, N., Classical and quantum conformal field theory, Comm. Math. Phys., 123, 177-254 (1989) · Zbl 0694.53074
[11] Rocha-Caridi, A.; Wallach, N. R., Highest weight modules over graded Lie algebras: Resolutions, filtrations, and character formulas, Trans. Amer. Math. Soc., 277, 133-162 (1983) · Zbl 0512.17007
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