On the combinatorics of unramified admissible modules

Details On the combinatorics of unramified admissible modules On the combinatorics of unramified admissible modules

2004-02-20

arxiv.org/abs/math/0402335v2

Publ. Res. Inst. Math. Sci. 42 no.2 589--603 (2006)

Mathematics

Representation Theory

v2. added a section about equivariant derived category and fixed a name about Soergel's question, 15pp, to appear in Publ. RIM

Scientific paper

We construct a certain topological algebra $\Ext ^{\sharp}_{G ^{\vee}} X (\chi)$ from a Deligne-Langlands parameter space $X (\chi)$ attached to the group of rational points of a connected split reductive algebraic group $G$ over a non-Archimedean local field $\mathbb K$. Then we prove the equivalence between the category of continuous modules of $\Ext ^{\sharp}_{G ^{\vee}} X (\chi)$ and the category of unramified admissible modules of $G (\mathbb K)$ with a generalized infinitesimal character corresponding to $\chi$. This is an analogue of Soergel's conjecture which concerns the real reductive setting.

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