Th. Weigel

The Euler characteristic of a Hecke algebra

It is shown that the Euler characteristic $χ_{(\mathcal{H},\mathcal{B},ε_q)}$ of a $\mathbb{Z}[[q]]$-Hecke algebra $\mathcal{H}$ associated with a finitely generated Coxeter group $(W,S)$ coincides with $p_{(W,S)}(q)^{-1}$, where $p_{(W,S)}(t)$ is the Poincaré series of $(W,S)$.