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arXiv · 1210.4307

Linear and Shalika local periods for the mirabolic group, and some consequences

Nadir Matringe
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Abstract

Using linear periods on the mirabolic subgroup of $GL(n,F)$, for $F$ a non archimedean local field, we give a list of the maximal Levi subgroups of $GL(n,F)$ which can distinguish a discrete series, and a generic representation. We also obtain the functional equation of the local exterior-square $L$-function of a generic representation of $GL(n,F)$ when $n=2m$ is even. Then we discuss the relation between Shalika models and local models for representations of $GL(2m,F)$. Finally we give a necessary and sufficient condition on the cuspidal representation $ρ$ for a generalised Steinberg representation $St_k(ρ)$ of $GL(2m,F)$ to have a local model.

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Nadir Matringe. 2018-07-31. Linear and Shalika local periods for the mirabolic group, and some consequences. https://arxiv.org/abs/1210.4307

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