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Harish-Chandra pairs in the Verlinde category in positive characteristic

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arxiv 1909.11240 v2 pith:SRP34DF7 submitted 2019-09-25 math.RT math.AGmath.GRmath.RA

Siddharth Venkatesh This is my paper · ORCID
classification math.RTmath.AGmath.GRmath.RA
keywords categoryverlindeequivalenceharish-chandrapairsrepresentationaffinearticle
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abstract

In this article, we prove that the category of affine group schemes of finite type in the Verlinde category is equivalent to the category of Harish-Chandra pairs in the Verlinde category. Subsequently, we extend this equivalence to an equivalence between corresponding representation categories and then study some consequences of this equivalence to the representation theory of $GL(L)$, with $L$ a simple object in the Verlinde category.

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  1. The highest weight theory for Representations of General Linear groups in the Verlinde categories in positive characteristic

    math.RT 2025-01 conditional novelty 6.0 of 10

    The paper proves that changing the Borel subgroup for GL(X) in Ver_p is governed by lowest weights of GL(L_m|L_n), computed via circular weight and cap diagrams.

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