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• W2963751203 abstract "Let $G$ be an orthogonal, symplectic or unitary group over a non-archimedean local field of odd residual characteristic. This paper concerns the study of the “wild part” of an irreducible smooth representation of $G$ , encoded in its “semisimple character”. We prove two fundamental results concerning them, which are crucial steps toward a complete classification of the cuspidal representations of $G$ . First we introduce a geometric combinatorial condition under which we prove an “intertwining implies conjugacy” theorem for semisimple characters, both in $G$ and in the ambient general linear group. Second, we prove a Skolem–Noether theorem for the action of $G$ on its Lie algebra; more precisely, two semisimple elements of the Lie algebra of $G$ which have the same characteristic polynomial must be conjugate under an element of $G$ if there are corresponding semisimple strata which are intertwined by an element of $G$ ." @default.
• W2963751203 created "2019-07-30" @default.
• W2963751203 creator A5031675561 @default.
• W2963751203 creator A5081054934 @default.
• W2963751203 date "2018-07-16" @default.
• W2963751203 modified "2023-09-23" @default.
• W2963751203 title "INTERTWINING SEMISIMPLE CHARACTERS FOR -ADIC CLASSICAL GROUPS" @default.
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• W2963751203 doi "https://doi.org/10.1017/nmj.2018.23" @default.
• W2963751203 hasPublicationYear "2018" @default.
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