The Euler characteristic of a Hecke algebra

Abstract

It is shown that the Euler characteristic ${\chi }_{(\mathcal{H},\mathcal{B},{\epsilon }_q)}$ 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 $(W,S)$.

11 pages; J. Pure Appl. Algebra (2014)

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