
Title: A Reduction Method for Representations of the General Linear Supergroup
Speaker: Thorsten Heidersdorf, The Ohio State University
Abstract: We describe a method to reduce certain questions (like tensor product decomposition, dimension formulas) about finite dimensional representations of the algebraic supergroup GL(m|n) resp. the Lie superalgebra gl(m|n) to lower rank cases such as gl(m-r|n-r) for some r. This is done in the following way: To every representation and every odd nilpotent element of of gl(m|n) we associate an infinite complex whose cohomology groups are representations of gl(m-r,n-r). We compute the cohomology of this complex if the representation is irreducible and give applications.