Irreducible p-modular representations of unramified U(2,1)

2016/08/02 by Abdellatif, Ramla, Xu, Peng
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1608.00897

Abstract

Let E/F be a unramified quadratic extension of non-archimedean local fields of odd characteristic p, and G be the unramified unitary group U(2, 1)(E/F). For an irreducible smooth representation π of G over F_p, with an underlying irreducible smooth representation σ of a maximal compact open subgroup K, we prove that π admits eigenvectors for an appropriate Hecke operator T_σ, and we classify those π with non-zero eigenvalues for T_σ by a tree argument; as a corollary, we show π is supersingular if and only if it is supercuspidal.

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