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

Nadir Matringe

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

Representation Theory 2018-08-01 v6

Authors: Nadir Matringe

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 $\rho$ for a generalised Steinberg representation $St_k(\rho)$ of $GL(2m,F)$ to have a local model.

Keywords

mirabolic subgroup linear period Shalika period local L-function Steinberg representation

Cite

@article{arxiv.1210.4307,
  title  = {Linear and Shalika local periods for the mirabolic group, and some consequences},
  author = {Nadir Matringe},
  journal= {arXiv preprint arXiv:1210.4307},
  year   = {2018}
}

Comments

We corrected a minor mistake in the proof of Theorem 3.2. We modified the proof of previous Proposition 4.1., which was to allusive, and needed in fact some corrections. The argument in the proof of Theorem 4.1. to conclude that the epsilon factor is a unit was not correct, now it is

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

Abstract

Keywords

Cite

Comments

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