The non-projective part of modular representations of finite groups

Abstract: In a recent paper, Dave Benson and Peter Symonds introduced a new invariant for modular representations of a finite group. This invariant is a result of studying the asymptotics of the direct sum decomposition of the non-projective part of tensor powers of a finite dimensional representation of a finite group in prime characteristic. In this talk, we will see some interesting properties of this invariant. We will obtain a closed formula for computing the invariant for a family of modules of the symmetric group and for trivial source modules of a finite group. Benson and Symonds conjectured that the growth of the non-projective part of tensor powers of a module is linear recursive. We will also see some results towards this conjecture.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar