Irreducible modules for quasisimple groups that are imprimitive
by
Kay Magaard
Wayne State University, Detroit MI
Coauthors: Gerhard Hiss, RWTH Aachen, Germany, William Husen, Ohio State University, Columbus OH

Let G be a quasisimple finite group, K an algebraically closed field and M an irreducible KG-module. We say that M is imprimitive with block stabilizer H subset G if there exists some KH-module M₀ such that M = Ind_H^G(M₀). If no such H exists we call M a primitive KG-module. Seitz proved that if G is of Lie type of characteristic p and if char(k) = p, then with four exceptions every irreducible KG-module is primitive. Djorkovic and Malzan proved a similar result for characteristic zero modules of alternating and symmetric groups. I will present joint work with Gerhard Hiss and William Husen that shows that the situation is very different when G is of Lie type of characteristic p and if char(K) =/= p. In fact in our case most irreducible KG-modules are imprimitive. I will also discuss how our results fit into the program of classifying maximal subgroups of classical groups.

Date received: March 13, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagg-23.