Non-Generic Unramified Representations in Metaplectic Covering Groups

2017/05/04 by Ginzburg, David
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1705.01770

Abstract

Let G^(r) denote the metaplectic covering group of the linear algebraic group G. In this paper we study conditions on unramified representations of the group G^(r) not to have a nonzero Whittaker function. We state a general Conjecture about the possible unramified characters χ such that the unramified sub-representation of Ind_B^(r)^G^(r)χδ_B^1/2 will have no nonzero Whittaker function. We prove this Conjecture for the groups GL_n^(r) with r≥ n-1, and for the exceptional groups G₂^(r) when r≠ 2.

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