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.
Citation
Shaun Stevens. "Semisimple characters for p-adic classical groups." Duke Math. J. 127 (1) 123 - 173, 15 March 2005. https://doi.org/10.1215/S0012-7094-04-12714-9
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