Representations Distinguished by Pairs of Exceptional Representations and a Conjecture of Savin

Eyal Kaplan

doi:10.1093/imrn/rnv150

Representations Distinguished by Pairs of Exceptional Representations and a Conjecture of Savin

Eyal Kaplan

Ohio State University

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Abstract

We study representations of GL_n appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series representations in terms of their inducing data. In particular, we complete the proof of a conjecture of Savin, relating distinguished spherical representations to the image of the tautological lift from a suitable classical group.

Original language	English
Pages (from-to)	604-643
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2016
Issue number	2
DOIs	https://doi.org/10.1093/imrn/rnv150
State	Published - 2016
Externally published	Yes

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© 2015 The Author(s). Published by Oxford University Press. All rights reserved.

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AB - We study representations of GLn appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series representations in terms of their inducing data. In particular, we complete the proof of a conjecture of Savin, relating distinguished spherical representations to the image of the tautological lift from a suitable classical group.

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Representations Distinguished by Pairs of Exceptional Representations and a Conjecture of Savin

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