An Extension of the Kazhdan-Lusztig Equivalence

Lin Chen; Yuchen Fu

An Extension of the Kazhdan-Lusztig Equivalence

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arxiv 2111.14606 v1 pith:EC7SFFYE submitted 2021-11-29 math.RT math.AG

Lin Chen , Yuchen Fu This is my paper · ORCID

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keywords equivalencecategorykazhdan-lusztigrepresentationsaffinealgebraalgebrasarxiv

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We prove a tamely ramified version of the Kazhdan-Lusztig equivalence using factorization algebras. More precisely, we establish an equivalence between the DG category of Iwahori-integrable affine Lie algebra representations and the DG category of representations of the "mixed" quantum group. This confirms a conjecture by D. Gaitsgory in arXiv:1810.09054 [math.RT].

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Non-vanishing of quantum geometric Whittaker coefficients
math.RT 2025-08 conditional novelty 7.0 of 10

For any adjoint reductive group at rational Kac-Moody level, cuspidal twisted D-modules with nilpotent singular support have at least one nonzero quantum Whittaker coefficient, proved microlocally.

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