On the Combinatorics of Unramified Admissible Modules

Abstract

We construct a certain topological algebra Ext �∨ 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 .T hen we prove the equivalence between the category of continuous modules of Ext �∨ X(χ )a nd 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.