Centers of Hecke Algebras of Complex Reflection Groups

Abstract

We provide a dual version of the Geck--Rouquier Theorem on the center of an Iwahori--Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank $2$, for which the symmetrising trace conjecture is known to be true, we provide a new faithful matrix model for their Hecke algebra $H$. These models enable concrete calculations inside $H$. For each of the eight groups, we compute an explicit integral basis of the center of $H$.

Final version; 14 pages. Appears in: Beiträge zur Algebra und Geometrie

References in corpus (1)

• The freeness and trace conjectures for parabolic Hecke subalgebras