Journal of Lie Theory

no. 3
Parahoric Induction and Chamber Homology for SL2
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 657-676
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).
DOI: 10.5802/jolt.854
Classification: 22E50, 19D55
Keywords: Representations of p-adic reductive groups, parabolic induction, chamber homology 
@article{JOLT_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},
     doi = {10.5802/jolt.854},
     zbl = {1327.22018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.854/}
}
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%J Journal of Lie Theory
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T. Crisp. Parahoric Induction and Chamber Homology for SL2. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 657-676. doi: 10.5802/jolt.854

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