TY - JOUR

T1 - Semisimple types for p-adic classical groups

AU - Miyauchi, Michitaka

AU - Stevens, Shaun

N1 - Funding Information:
This paper has been a long time coming. The second author would like to thank Muthu Krishnamurthy for asking the question which prompted him to get on and finish it. He would also like to thank Laure Blasco, Corinne Blondel and Van-Dinh Ngo for pointing out some mistakes in [] and especially Corinne Blondel for many useful discussions. This work was supported by the Engineering and Physical Sciences Research Council (grants GR/T21714/01, EP/G001480/1 and EP/H00534X/1).

PY - 2014/2

Y1 - 2014/2

N2 - We construct, for any symplectic, unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic, a type for each Bernstein component of the category of smooth representations, using Bushnell-Kutzko's theory of covers. Moreover, for a component corresponding to a cuspidal representation of a maximal Levi subgroup, we prove that the Hecke algebra is either abelian, or a generic Hecke algebra on an infinite dihedral group, with parameters which are, at least in principle, computable via results of Lusztig. In an appendix, we make a correction to the proof of a result of the second author: that every irreducible cuspidal representation of a classical group as considered here is irreducibly compactly-induced from a type.

AB - We construct, for any symplectic, unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic, a type for each Bernstein component of the category of smooth representations, using Bushnell-Kutzko's theory of covers. Moreover, for a component corresponding to a cuspidal representation of a maximal Levi subgroup, we prove that the Hecke algebra is either abelian, or a generic Hecke algebra on an infinite dihedral group, with parameters which are, at least in principle, computable via results of Lusztig. In an appendix, we make a correction to the proof of a result of the second author: that every irreducible cuspidal representation of a classical group as considered here is irreducibly compactly-induced from a type.

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U2 - 10.1007/s00208-013-0953-y

DO - 10.1007/s00208-013-0953-y

M3 - Article

AN - SCOPUS:84893793805

VL - 358

SP - 257

EP - 288

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -