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

  title={Cellular structures using \$\textbf\{U\}\_q\$-tilting modules},
  author={Henning Haahr Andersen and Catharina Stroppel and Daniel Tubbenhauer},
  journal={arXiv: Quantum Algebra},
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… 
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