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Representations of general linear groups and categorical actions of Kac-Moody algebras

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arxiv 1209.1067 v1 pith:5WYJUHFM submitted 2012-09-05 math.RT math.COmath.CT

Ivan Losev This is my paper · ORCID
classification math.RTmath.COmath.CT
keywords categoricalrepresentationsactionactionsalgebrasgeneralgroupskac-moody
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This is an expanded version of the lectures given by the author on the 3rd school "Lie algebras, algebraic groups and invariant theory" in Togliatti, Russia. In these notes we explain the concept of a categorical Kac-Moody action by studying an example of the category of rational representations of a general linear group in positive characteristic. We also deal with some more advanced topics: a categorical action on the polynomial representations and crystals of categorical actions.

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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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