Semisimple types for p-adic classical groups

Michitaka Miyauchi; Shaun Stevens

doi:10.1007/s00208-013-0953-y

Semisimple types for p-adic classical groups

Michitaka Miyauchi, Shaun Stevens

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	257-288
Number of pages	32
Journal	Mathematische Annalen
Volume	358
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-013-0953-y
Publication status	Published - 2014
Externally published	Yes

Fingerprint

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

Miyauchi, M., & Stevens, S. (2014). Semisimple types for p-adic classical groups. 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.

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

Research output: Contribution to journal › Article

Miyauchi, M & Stevens, S 2014, 'Semisimple types for p-adic classical groups', Mathematische Annalen, vol. 358, no. 1-2, pp. 257-288. https://doi.org/10.1007/s00208-013-0953-y

Miyauchi M, Stevens S. Semisimple types for p-adic classical groups. Mathematische Annalen. 2014;358(1-2):257-288. https://doi.org/10.1007/s00208-013-0953-y

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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10.1007/s00208-013-0953-y