Module categories for A_n web categories from A_n-1-buildings

2022/11/02 by Emily McGovern, McGovern, Emily
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2211.01149

openalex publication_date 2022/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We equip the category of vector bundles over the vertices of a locally finite A_n-1 building Δ with the structure of a module category over a category of type A_n webs in positive characteristic. This module category is a q-analogue of the Rep(SL_n) action on vector bundles over the sl_n weight lattice. We show our module categories are equivariant with respect to symmetries of the building, and when a group G acts simply transitively on the vertices of Δ this recovers the fiber functors constructed by Jones.

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