Tame cuspidal representations in non-defining characteristics
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Publication:6318826
DOI10.1307/MMJ/20217217arXiv1905.06374MaRDI QIDQ6318826
Publication date: 15 May 2019
Abstract: Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex supercuspidal representations yields smooth, irreducible, cuspidal representations over an arbitrary algebraically closed field R of characteristic different from p. Moreover, we prove that this construction provides all smooth, irreducible, cuspidal R-representations if p does not divide the order of the Weyl group of G.
Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Representations of Lie and linear algebraic groups over local fields (22E50) Linear algebraic groups over local fields and their integers (20G25)
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