Cocenters and representations of affine $0$-Hecke algebras

Abstract

In this paper, we study the relation between the cocenter $\overline{{\widetilde{\mathrm{ch}}}_0}$ and the finite dimensional representations of an affine $0$-Hecke algebra ${\widetilde{\mathrm{ch}}}_0$. As a consequence, we obtain a new criterion on the supersingular modules: a (virtual) module of ${\widetilde{\mathrm{ch}}}_0$ is supersingular if and only if its character vanishes on the non-supersingular part of $\overline{{\widetilde{\mathrm{ch}}}_0}$.

18 pages

References in corpus (1)

• Minimal length elements in conjugacy classes of extended affine Weyl group

Cited by in corpus (1)

• Cocenter of $p$-adic groups, II: induction map