On the Combinatorics of Unramified Admissible Modules

Abstract

We construct a certain topological algebra Ext#_G_∨ X(χ) from a Deligne–Langlands parameter space X(χ) attached to the group of rational points of a connected split reductive algebraic group G over a non-Archimedean local field K. Then we prove the equivalence between the category of continuous modules of Ext#_G_∨ X(χ) and the category of unramified admissible modules of G(K) with a generalized infinitesimal character corresponding to χ. This is an analogue of Soergel’s conjecture which concerns the real reductive setting.