Criteria for the Existence of Cuspidal Theta Representations

Abstract

Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal theta representation is one which is equal to the local twisted theta representation at almost all places. Cuspidal theta representations are known to exist but only for covers of $G{L}_j$, $j\le 3$. In this paper we establish necessary conditions for the existence of cuspidal theta representations on the $r$-fold metaplectic cover of the general linear group of arbitrary rank.

16 pages

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