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
crisp@math.ku.dk
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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