Semisimple types for p-adic classical groups

Michitaka Miyauchi, Shaun Stevens

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)257-288
Number of pages32
JournalMathematische Annalen
Volume358
Issue number1-2
DOIs
Publication statusPublished - 2014
Externally publishedYes

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P-adic Groups
Hecke Algebra
Classical Groups
Semisimple
Dihedral group
Infinite Groups
Orthogonal Group
Locally Compact
Local Field
Irreducible Representation
Odd
Subgroup
Cover

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Mathematische Annalen, Vol. 358, No. 1-2, 2014, p. 257-288.

Research output: Contribution to journalArticle

Miyauchi, Michitaka ; Stevens, Shaun. / Semisimple types for p-adic classical groups. In: Mathematische Annalen. 2014 ; Vol. 358, No. 1-2. pp. 257-288.
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