University of Sydney Algebra Seminar

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).