CU Algebraic Lie Theory Seminar

An analytic approach to the representation theory of finite groups

Marty Walter, CU

Abstract

There are many examples of non-isomorphic finite groups of the same order that have the ``same representation theory (over the complex numbers).'' By this we mean that the groups in question have the same number of irreducible representations of a given dimension, and the tensor products of any two such representations decompose in like fashion. We look for properties of the ``fine structure'' of the representations which allow us to distinguish said groups. The search leads us to consider cohomology, notions of positivity and partial orderings, infinitely divisible laws in probability theory and other interesting topics. (The search is not over.)