Semisimplification of the category of tilting modules for GL_n

Abstract

We describe the semisimplification of the monoidal category of tilting modules for the algebraic group GL_n in characteristic p > 0. In particular, we compute the dimensions of the indecomposable tilting modules modulo p.

arXiv commentThis version corrects a minor mistake in the proof of Lemma 3.4 in the published version

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• A new approach to the representation theory of the partition category
• The $q$-Schur category and polynomial tilting modules for quantum $G{L}_n$
• Webs of Type P