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“The modular character
ring and its associated

monomial Burnside ring, part I”

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LAURENCE BARKER

(Bilkent University)

__Abstract:__ Group
representation theory is the study of linear symmetries of modules, especially
vector spaces (the appalling name of the topic emerged from an accident of
history.) When the scalar field has characteristic zero,
the character ring is an integer lattice whose points are the virtual modules
of the group algebra, up to isomorphism. Modular representation theory concerns
the case where the scalar field is of prime characteristic (another appalling accident.)
In this case, the character ring is an integer lattice whose points are the
virtual modules up to Grothendieck equivalence; this
detects the simple composition factors, up to multiplicity. We shall give an introduction
to the modular scenario, and we shall explain how, for an algebraically closed
scalar field, the character
ring can be described in terms of a corresponding monomial Burnside ring.

Date : September 28, 2009 (Monday)

Time : 14:40-15:30

Place: Seminar Room SA-141