The cocenter of graded affine Hecke algebra and the density theorem

TL;DR

This paper establishes a basis for the cocenter of graded affine Hecke algebras with arbitrary parameters, proving the density theorem and trace Paley-Wiener theorem, which clarify the structure of traces and forms in this algebraic setting.

Contribution

It provides a basis for the cocenter of graded affine Hecke algebras and proves the density and trace Paley-Wiener theorems in this context.

Findings

Kernel of the trace map equals the commutator subspace.

Image of the trace map is the space of good forms.

Established a basis for the cocenter of graded affine Hecke algebras.

Abstract

We determine a basis of the (twisted) cocenter of graded affine Hecke algebras with arbitrary parameters. In this setting, we prove that the kernel of the (twisted) trace map is the commutator subspace (Density theorem) and that the image is the space of good forms (trace Paley-Wiener theorem).