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Journal of Lie Theory 25 (2015), No. 3, 657--676
Copyright Heldermann Verlag 2015

Parahoric Induction and Chamber Homology for SL2

Tyrone Crisp
Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen O, Denmark

We consider the special linear group G = SL2 over a p-adic field, and its diagonal torus M ≡ GL1. Parabolic induction of representations from M to G induces a map in equivariant homology, from the Bruhat-Tits building of M to that of G. We compute this map at the level of chain complexes, and show that it is given by parahoric induction (as defined by J.-F. Dat).

Keywords: Representations of p-adic reductive groups, parabolic induction, chamber homology.

MSC: 22E50, 19D55

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