Geodesic
Parahoric Induction and Chamber Homology for SL2
Journal of Lie theory, Tome 25 (2015) no. 3, pp. 657-676
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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).
Classification : 22E50, 19D55
Mots-clés : Representations of p-adic reductive groups, parabolic induction, chamber homology 
@article{JLT_2015_25_3_JLT_2015_25_3_a1,
     author = {T. Crisp},
     title = {Parahoric {Induction} and {Chamber} {Homology} for {SL\protect\textsubscript{2}}},
     journal = {Journal of Lie theory},
     pages = {657--676},
     year = {2015},
     volume = {25},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a1/}
}
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T. Crisp. Parahoric Induction and Chamber Homology for SL2. Journal of Lie theory, Tome 25 (2015) no. 3, pp. 657-676. http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a1/