Clarify relation between graded affine Hecke algebra standard modules and p-adic standard representations

Ascertain a precise and documented correspondence between “standard modules” for graded affine Hecke algebras and standard representations of p-adic groups, including a clear articulation of the mapping and hypotheses under which it holds.

Background

Solleveld’s work proves analogues of p-KLH for graded affine Hecke algebras, extending the reach beyond earlier settings. However, a fully detailed account connecting these standard modules to p-adic standard representations—and thereby to geometric multiplicity formulas—has not yet appeared.

The authors note that while such a correspondence should follow from previous results, its explicit articulation in the literature remains desirable for the p-adic KLH program.