On the Combinatorics of Unramified Admissible Modules

  • Syu Kato

    University of Tokyo, Japan


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.

Cite this article

Syu Kato, On the Combinatorics of Unramified Admissible Modules. Publ. Res. Inst. Math. Sci. 42 (2006), no. 2, pp. 589–603

DOI 10.2977/PRIMS/1166642117