## University of Sydney Algebra Seminar

# Tommaso Terragni (University of Sydney)

## Friday 26th October, 12:05-12:55pm, Carslaw 175

### Euler characteristic of Hecke algebras

By an old result of Serre, (finitely generated) Coxeter groups admit an Euler characteristic, and this can be computed by *evaluating* the inverse of the Poincaré series at \(1\). The Poincaré series itself can be computed through a recursive, alternating-sum formula (Steinberg, Solomon), which is in general meaningless for the corresponding evaluation.

Thus, the Poincaré series looks like an Euler character, much more than its evaluation does.

In this talk we show that it is indeed the case: the Poincaré series of the Coxeter system appears as the (suitably defined) Euler characteristic of a (suitably defined) Hecke algebra.