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. 589–603DOI 10.2977/PRIMS/1166642117