Cellular structures using $\textbf{U}_q$tilting modules
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 nonsemisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinitedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 arXiv:
 arXiv:1503.00224
 Bibcode:
 2015arXiv150300224H
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory
 EPrint:
 31 pages, lots of figures, substantially rewritten (following the suggestions of some referees), changed numbering, comments welcome