Abstract
We give complete proofs of the K-theoretic construction of the quantized enveloping algebra of affine gl(n) sketched in [GV].
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[A] S. Ariki,On the decomposition number of the Hecke algebra of G(m, 1, n), J. Math. Kyoto Univ.36 (1996), 789–808.
[BLM] A. Beilinson, G. Lusztig, and R. MacPherson,A geometric setting for quantum groups, Duke Math. J.61 (1990), 655–675.
[CG] N. Chriss, and V. Ginzburg,Representation Theory and Complex Geometry, Birkhauser, 1997.
[CP1] V. Chari, and A. Pressley,Quantum affine algebras and affine Hecke algebras, Pacific J. Math.174 (1996), 295–326.
[CP2] V. Chari, and A. Pressley,A Guide to Quantum Groups, Cambridge University Press, 1994.
[D] В. Г. Дринфельд,Новая реализация янгианов и квантованных аффинных алгебр, Доклады АН СССР296:1 (1988), 13–17. English translation: V. Drinfeld,A new realization of Yangians and quantized affine algebras, Soviet. Math. Dokl.36 (1988), 212–216.
[DF] J. Ding, J. Frenkel and I. Frenkel,Isomorphism of two realizations of the quantum affine algebra \(U_q (\widehat{\mathfrak{g}\mathfrak{l}}(n))\), Comm. Math. Phys.156 (1994), 277–300.
[GRV] V. Ginzburg, N. Reshetikhin, and E. Vasserot,Quantum groups and flag varieties, Contemp. Math.175 (1994), 101–130.
[GV] V. Ginzburg and E. Vasserot,Langlands reciprocity for affine quantum groups of type A n, Internat. Math. Res. Notices3 (1993), 67–85.
[KL] D. Kazhdan and G. Lusztig,Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math.87 (1987), 153–215.
[M] I. G. MacDonald,Symmetric Functions and Hall Polynomials, Oxford University Press, 1995. Russian translation of the edition of 1979: И. Макдональд, Симметрические функгии и тнозочлены Холла, Мир, Москва, 1985.
[V] E. Vasserot,Representations de groupes quantiques et permutations, Annles Sci. ENS26 (1993), 747–773.
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The author is partially supported by EEC grant no. ERB FMRX-CT97-0100.
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Vasserot, E. Affine quantum groups and equivariantK-theory. Transformation Groups 3, 269–299 (1998). https://doi.org/10.1007/BF01236876
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DOI: https://doi.org/10.1007/BF01236876