The noncommutativity of Hecke algebras associated to Weyl groups

Abstract

We prove that the Hecke algebra H ( W , W J ) \mathcal {H}(W,{W_J}) , where W is a Weyl group of spherical type and W J {W_J} is a standard parabolic subgroup of W of corank ≥ 2 \geq 2 , is noncommutative.