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Intertwining and Supercuspidal Types for p ‐Adic Classical Groups
Author(s) -
Stevens Shaun
Publication year - 2001
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/83.1.120
Subject(s) - mathematics , maximal torus , torus , symplectic geometry , unitary state , character (mathematics) , fixed point , pure mathematics , involution (esoterism) , classical group , reductive group , combinatorics , lie group , mathematical analysis , group theory , lie algebra , geometry , fundamental representation , politics , political science , law , weight
Let F be a non‐archimedean local field of residual characteristic different from 2, and let G be a unitary, symplectic or orthogonal group, considered as the fixed point subgroup inG ~ = G L ( N , F ) of an involution σ. We generalize the notion of a simple character forG ~ , which was introduced by Bushnell and Kutzko [Annals of Mathematics Studies 129 (Princeton University Press, 1993)], to define semisimple characters. Given a semisimple character θ forG ~fixed by σ, we transfer it to a character θ − for G and calculate its intertwining. If the torus associated to θ − is maximal compact, we obtain supercuspidal representations of G , which are new if the torus is split only over a wildly ramified extension. 2000 Mathematics Subject Classification : 22E50.