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Radically filtered quasi-hereditary algebras and rigidity of tilting modules

Published online by Cambridge University Press:  01 March 2017

AMIT HAZI
AMIT HAZI*
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB. e-mail: A.Hazi@dpmms.cam.ac.uk
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Abstract

Let A be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) 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 show that the restricted tilting modules for SL4(K) are rigid, where K is an algebraically closed field of characteristic p ≥ 5.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 2 , September 2017 , pp. 265 - 288
Copyright
Copyright © Cambridge Philosophical Society 2017 

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