An Extension of the Kazhdan-Lusztig Equivalence

2021/11/29 by Lin Chen, Chen, Lin, Yuchen Fu +1 · 1 citation
Mathematics · #17B37 #17B67 (Primary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2111.14606

openalex publication_date 2021/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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].

Citations

• Factorizable sheaves and quantum groups
• Outline of the proof of the geometric Langlands conjecture for GL(2)
• Affine Beilinson-Bernstein localization at the critical level for GL₂

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