Duality for Ext-groups and extensions of discrete series for graded Hecke algebras
arXiv:1410.1495 · doi:10.1016/j.aim.2016.03.002
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.
36 pages, v2: Some results and proofs are improved. Sections 5,6,7 in v2 are new. Section 5 in v1 is completely removed and may appear elsewhere; v3: close to published version