Duality for Ext-groups and extensions of discrete series for graded Hecke algebras

TL;DR

This paper establishes a duality for Ext-groups in graded affine Hecke algebra modules and proves that higher Ext-groups between discrete series vanish, using explicit projective resolutions and algebraic methods.

Contribution

It introduces a duality result for Ext-groups in the context of graded affine Hecke algebras and provides an algebraic proof for the vanishing of higher Ext-groups between discrete series.

Findings

Duality for Ext-groups established

Higher Ext-groups between discrete series vanish

Explicit projective resolutions used in proofs

Abstract

In this paper, we study extensions of graded affine Hecke algebra modules. In particular, based on an explicit projective resolution on graded affine Hecke algebra modules, we prove a duality result for Ext-groups. This duality result with an Ind-Res resolution gives an algebraic proof of the fact that all higher Ext-groups between discrete series vanish.