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arXiv · 1507.07413

Criteria for the Existence of Cuspidal Theta Representations

Solomon Friedberg·David Ginzburg
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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 $GL_j$, $j\leq 3$. 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.

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Solomon Friedberg, David Ginzburg. 2015-07-27. Criteria for the Existence of Cuspidal Theta Representations. https://doi.org/10.1007/s40993-016-0046-6

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