# Rigidity of tilting modules

• Amit Hazi, University of Cambridge
• Friday 23 January 2015, 15:00-16:00
• CMS, MR14.

A quasi-hereditary algebra is an algebra whose modules behave similarly to representations of an algebraic group or to modules in category $\mathcal{O}$, with standard modules and costandard modules taking the place of Weyl modules and dual Weyl modules, or Verma modules and dual Verma modules. A tilting module over a quasi-hereditary algebra is a module with a filtration by standard modules and another filtration by costandard modules. We prove that in many cases, a tilting module is rigid (i.e. it has a unique semisimple filtration, or equivalently the radical and socle series coincide) if it does not have certain subquotients whose composition factors extend more than one layer in the radical series or the socle series. We apply this theorem to give new results about the radical series of some tilting modules for $SL_4(K)$, where $K$ is a field of positive characteristic.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.