Some power series involving involutions in Coxeter groups

TL;DR

This paper explores a power series related to involutions in Coxeter groups, expressing it through the Poincare series, extending known results from finite groups to more general cases.

Contribution

It introduces a new expression for a power series involving involutions in Coxeter groups using the Poincare series, generalizing previous finite group results.

Findings

Power series involving involutions can be expressed via Poincare series.

Extension of known finite Coxeter group results to infinite cases.

Provides a new algebraic relationship in Coxeter group theory.

Abstract

Let W be a Coxeter group. We show that a certain power series involving a sum over all involutions in W can be expressed in terms of the Poincare series of W. (The case where W is finite is already known,)