Vector bundles on quantum conjugacy classes

2022/01/12 by Andrey Mudrov, Mudrov, Andrey
Mathematics · #17B10 #17B37 #53D55 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2201.04568

openalex publication_date 2022/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrakg be a simple complex Lie algebra of a classical type and U_q(\mathfrakg) the corresponding Drinfeld-Jimbo quantum group at q not a root of unity. With every point t of the fixed maximal torus T of an algebraic group G with Lie algebra \mathfrakg we associate an additive category O_q(t) of U_q(\mathfrakg)-modules that is stable under tensor product with finite-dimensional quasi-classical U_q(\mathfrakg)-modules. We prove that O_q(t) is essentially semi-simple and use it to explicitly quantize equivariant vector bundles on the conjugacy class of t.

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