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SUMMARY:Rigidity of tilting modules - Amit Hazi\, University of Cambridge
DTSTART:20150123T150000Z
DTEND:20150123T160000Z
UID:TALK57604@talks.cam.ac.uk
CONTACT:Julian Brough
DESCRIPTION:A quasi-hereditary algebra is an algebra whose modules behave 
 similarly to representations of an algebraic group or to modules in catego
 ry $\\mathcal{O}$\, with standard modules and costandard modules taking th
 e 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 modul
 e with a filtration by standard modules and another filtration by costanda
 rd 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 so
 cle series coincide) if it does not have certain subquotients whose compos
 ition factors extend more than one layer in the radical series or the socl
 e series. We apply this theorem to give new results about the radical seri
 es of some tilting modules for $SL_4(K)$\, where $K$ is a field of positiv
 e characteristic.
LOCATION:CMS\, MR14
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