Tame cuspidal representations in non-defining characteristics

2019/05/15 by Fintzen, Jessica · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1905.06374

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.

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