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arXiv · 1510.06213

Shalika periods and parabolic induction for GL(n) over a non archimedean local field

Nadir Matringe
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Abstract

Let $F$ be a non archimedean local field, and $n_1$ and $n_2$ two positive even integers. We prove that if $π_1$ and $π_2$ are two smooth representations of $GL(n_1,F)$ and $GL(n_2,F)$ respectively, both admitting a Shalika period, then the normalised parabolically induced representation $π_1\times π_2$ also admits a Shalika period. Combining this with the results of \cite{M-localBF}, we obtain as a corollary the classification of generic representations of $GL(n,F)$ admitting a Shalika period when $F$ has characteristic zero. This result is relevant to the study of the Jacquet-Shalika exterior square $L$ factor.

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BibTeXRIS

Nadir Matringe. 2016-10-08. Shalika periods and parabolic induction for GL(n) over a non archimedean local field. https://doi.org/10.1112/blms.12020

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