### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 257-288 |

Number of pages | 32 |

Journal | Mathematische Annalen |

Volume | 358 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2014 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Annalen*,

*358*(1-2), 257-288. https://doi.org/10.1007/s00208-013-0953-y

**Semisimple types for p-adic classical groups.** / Miyauchi, Michitaka; Stevens, Shaun.

Research output: Contribution to journal › Article

*Mathematische Annalen*, vol. 358, no. 1-2, pp. 257-288. https://doi.org/10.1007/s00208-013-0953-y

}

TY - JOUR

T1 - Semisimple types for p-adic classical groups

AU - Miyauchi, Michitaka

AU - Stevens, Shaun

PY - 2014

Y1 - 2014

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.

UR - http://www.scopus.com/inward/record.url?scp=84893793805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893793805&partnerID=8YFLogxK

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 -