A Conjectural Extension of the Kazhdan–Lusztig Equivalence
Dennis GaitsgoryHarvard University, Cambridge, USA
A theorem of Kazhdan and Lusztig establishes an equivalence between the category of -integrable representations of the Kac--Moody algebra at a negative level and the category 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 , involves Lusztig's version of the quantum group for the Borel and the De Concini–Kac version for the negative Borel.
Cite this article
Dennis Gaitsgory, A Conjectural Extension of the Kazhdan–Lusztig Equivalence. Publ. Res. Inst. Math. Sci. 57 (2021), no. 3/4, pp. 1227–1376DOI 10.4171/PRIMS/57-3-14