#### Vol. 286, No. 1, 2017

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Local symmetric square $L$-factors of representations of general linear groups

### Shunsuke Yamana

Vol. 286 (2017), No. 1, 215–256
##### Abstract

This paper develops a theory of local symmetric square $L$-factors of representations of general linear groups. We will prove a certain characterization of a pole of symmetric square $L$-factors of square-integrable representations, the uniqueness of certain trilinear forms and the nonexistence of Whittaker models of higher exceptional representations.

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##### Keywords
symmetric square $L$-factors, exceptional representations, distinguished representations
Primary: 11F66
Secondary: 11F70
##### Milestones
Received: 30 April 2015
Revised: 3 September 2015
Accepted: 14 June 2016
Published: 9 December 2016
##### Authors
 Shunsuke Yamana Department of Mathematics Kyoto University Kitashirakawa Oiwake-cho Sakyo-ku Kyoto 606-8502 Japan Hakubi Center Kyoto University Yoshida-honmachi Sakyo-ku Kyoto 606-8501 Japan