Title: Non-Generic Unramified Representations in Metaplectic Covering Groups,
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 $\chi$ such that
the unramified sub-representation of
$Ind_{B^{(r)}}^{G^{(r)}}\chi\delta_B^{1/2}$ will have no nonzero Whittaker
function. We prove this Conjecture for the groups $GL_n^{(r)}$ with $r\ge n-1$,
and for the exceptional groups $G_2^{(r)}$ when $r\ne 2$.