“The modular character
ring and its associated
monomial Burnside ring, part I”
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.
Place: Seminar Room SA-141