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arXiv · 1810.09054

A conjectural extension of the Kazhdan-Lusztig equivalence

Dennis Gaitsgory
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Abstract

A theorem of Kazhdan and Lusztig establishes an equivalence between the category of G(CO)-integrable representations of the Kac-Moody algebra \hat{g}_{-\kappa} at a negative level -\kappa and the category \Rep_q(G) of (algebraic) representations of the "big" (a.k.a. Lusztig's) quantum group. In this paper we propose a conjecture that describes the category of Iwahori-integrable Kac-Moody modules. The corresponding object on the quantum group side, denoted Rep^{mxd}_q(G), involves Lusztig's version of the quantum group for the Borel and the De Concini-Kac version for the negative Borel.

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Dennis Gaitsgory. 2018-10-22. A conjectural extension of the Kazhdan-Lusztig equivalence. https://arxiv.org/abs/1810.09054

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