The non-projective part of the tensor powers of a module

Abstract

Let $M$ be a finite dimensional modular representation of a finite group $G$. We consider the generating function for the non-projective part of the tensor powers of $M$, and we write ${\gamma }_G(M)$ for the reciprocal of the radius of convergence of this power series. We investigate the properties of the invariant ${\gamma }_G(M)$, using tools from representation theory, and from the theory of commutative Banach algebras.

Cited by in corpus (2)

• Growth rates of the number of indecomposable summands in tensor powers
• Asymptotics in finite monoidal categories