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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2015
- arXiv:
- arXiv:1503.00224
- Bibcode:
- 2015arXiv150300224H
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Rings and Algebras;
- Mathematics - Representation Theory
- E-Print:
- 31 pages, lots of figures, substantially rewritten (following the suggestions of some referees), changed numbering, comments welcome