Vol. 292, No. 1, 2018

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ISSN: 0030-8730
Cellular structures using $\boldsymbol{U}_q$-tilting modules

Henning Haahr Andersen, Catharina Stroppel and Daniel Tubbenhauer

Vol. 292 (2018), No. 1, 21–59
Abstract

We use the theory of Uq-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group Uq attached to a Cartan matrix and include the nonsemisimple 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 semisimplicity criterion for centralizer algebras, and we recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.

Keywords
cellular algebras, cellular bases, tilting modules, quantum enveloping algebras
Mathematical Subject Classification 2010
Primary: 17B10, 17B37, 20G05
Secondary: 16S50, 20C08, 20G42
Milestones
Received: 1 October 2016
Revised: 22 February 2017
Accepted: 2 May 2017
Published: 22 September 2017
Authors
Henning Haahr Andersen
QGM, Det Naturvidenskabelige Fakultet
Aarhus Universitet
Aarhus
Denmark
Catharina Stroppel
Mathematisches Institut
Universität Bonn
Bonn
Germany
Daniel Tubbenhauer
Mathematisches Institut
Universität Bonn
Bonn
Germany