Cocenters of Hecke-Clifford and spin Hecke algebras

TL;DR

This paper identifies a basis for the cocenter of degenerate affine Hecke-Clifford and spin Hecke algebras in classical types, advancing understanding of their algebraic structures.

Contribution

It provides the first explicit basis for the cocenter of these specialized Hecke algebras, linking Hochschild homology to algebraic representation theory.

Findings

Established a basis for the cocenter of the algebras.

Connected the cocenter structure to Hochschild homology.

Enhanced understanding of algebraic properties in classical types.

Abstract

We determine a basis of the cocenter (i.e., the zeroth Hochschild homology) of the degenerate affine Hecke-Clifford and spin Hecke algebras in classical types.