# James Parkinson (University of Sydney)

## Friday 1 April, 12:05-12:55pm, Carslaw 175

### A classification of commutative parabolic Hecke algebras

Let $$W$$ be an arbitrary Coxeter group and let $$H$$ be the associated generic Hecke algebra with basis $$T_w$$, $$w\in W$$. Let $$W_J$$ be a parabolic subgroup of $$W$$ and let $$1_J$$ be the sum of the basis elements $$T_w$$ with $$w\in W_J$$. In this talk we classify the pairs $$(W,J)$$ for which the $$J$$-parabolic Hecke algebra $$H_J=1_J H 1_J$$ is commutative. This is joint work with Peter Abramenko (Virginia) and Hendrik Van Maldeghem (Ghent).