Category O for hybrid quantum groups and non-commutative Springer resolutions

2023/08/14 by Quan Situ, Situ, Quan
Mathematics · Physics and Astronomy · #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2308.07028

openalex publication_date 2023/08/14 · openalex created_date 2023/08/16 · openalex updated_date 2026/07/28

Abstract

The hybrid quantum group was firstly introduced by Gaitsgory, whose category O can be viewed as a quantum analogue of BGG category O. We give a coherent model for its principal block at roots of unity, using the non-commutative Springer resolution defined by Bezrukavnikov--Mirković. In particular, the principal block is derived equivalent to the affine Hecke category. As an application, we endow the principal block with a canonical grading, and show that the graded multiplicity of simple module in Verma module is given by the generic Kazhdan--Lusztig polynomial.

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