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arXiv · 1503.00224

Cellular structures using $\textbf{U}_q$-tilting modules

Henning Haahr Andersen·Catharina Stroppel·Daniel Tubbenhauer
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Abstract

We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicty criterion for centralizer algebras, and recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.

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Henning Haahr Andersen, Catharina Stroppel, Daniel Tubbenhauer. 2015-03-01. Cellular structures using $\textbf{U}_q$-tilting modules. https://doi.org/10.2140/pjm.2018.292.21

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