Duke Mathematical Journal

Semisimple characters for p-adic classical groups

Shaun Stevens

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Abstract

Let G be a unitary, symplectic, or orthogonal group over a non-Archimedean local field of residual characteristic different from 2, considered as the fixed-point subgroup in a general linear group $\widetilde{G}$ of an involution. Following [8] and [12], we generalize the notion of a semisimple character for $\widetilde{G}$ and for G. In particular, following the formalism of [4], we show that these semisimple characters have certain functorial properties. Finally, we show that any positive level supercuspidal representation of G contains a semisimple character.

Article information

Source
Duke Math. J., Volume 127, Number 1 (2005), 123-173.

Dates
First available in Project Euclid: 4 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1109963912

Digital Object Identifier
doi:10.1215/S0012-7094-04-12714-9

Mathematical Reviews number (MathSciNet)
MR2126498

Zentralblatt MATH identifier
1063.22018

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Citation

Stevens, Shaun. Semisimple characters for p -adic classical groups. Duke Math. J. 127 (2005), no. 1, 123--173. doi:10.1215/S0012-7094-04-12714-9. https://projecteuclid.org/euclid.dmj/1109963912


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