Hecke modules and supersingular representations of U(2,1)

2012/04/05 by Koziol, Karol, Xu, Peng
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1204.1273

Abstract

Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-p-Iwahori-Hecke algebra H_C(G,I(1)), where G is the unramified unitary group U(2,1)(E/F) in three variables. Using this description when C is the algebraic closure of \mathbbF_p, we define supersingular Hecke modules and show that the functor of I(1)-invariants induces a bijection between irreducible nonsupersingular mod-p representations of G and nonsupersingular simple right H_C(G,I(1))-modules. We then use an argument of Paskunas to construct supersingular representations of G.

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