arXiv subjects

Nadir Matringe

Publications and source records attributed to Nadir Matringe.

59 records · Page 4Linked to original sources

arXiv2009

Distinction of some induced representations

Let $K/F$ be a quadratic extension of $p$-adic fields, $σ$ the nontrivial element of the Galois group of $K$ over $F$, and $π$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $π^{\vee}$ the smooth contragredient of $π$, and by $π^σ$ the representation $π\circ σ$, we show that the representation of $GL(2n, K)$ obtained by normalized parabolic induction of the representation $π^\vee \otimes π^σ$ is distinguished with respect to $GL(2n,F)$. This is a step towards the classification of distinguished generic representations of general linear groups over $p$-adic fields.

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arXiv2009

Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields

Let $K/F$ be a quadratic extension of p-adic fields. The Bernstein-Zelevinsky's classification asserts that generic representations are parabolically induced from quasi-square-integrable representations. We show, following a method developed by Cogdell and Piatetski-Shapiro, that the equality of the Rankin-Selberg type Asai $L$-function of generic representations of $GL(n,K)$ and of the Asai $L$-function of the Langlands parameter, is equivalent to the truth of a conjecture about classification of distinguished generic representations in terms of the inducing quasi-square-integrable representations. As the conjecture is true for principal series representations, this gives the expression of the Asai L-function of such representations.

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arXiv2008

Distinguished representations and exceptional poles of the Asai-L-function

In this article, we proove that it is equivalent for a generic irreducible representation of GL(n,K), with K a p-adic field, to be distinguished, and for its Rankin-Selberg Asai L-function to have an exceptional pole at zero. This extends a criterion of Kable claiming that a discrete series representation is distinguished if and only if its Asai L-function has a pole at zero. As an application we compute by local methods Asai L-functions of ordinary representations of GL(2,K), in particular we give a formula for Asai L-functions of principal series representations of GL(2,K).

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arXiv2008

Distinguished principal series representations for GLn over a p-adic field

In the following article, we give a description of the distingushed irreducible principal series representations of the general linear group over a p-adic field in terms of inducing datum. This provides a counter-example to a conjecture of Jacquet about distinction (Conjecture 1 in U.K Anandavardhanan, "Distinguished non-Archimedean representations ", Proc. Hyderabad Conference on Algebra and Number Theory, 2005, 183-192).

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arXiv2006

Distinguished dihedral representations of GL(2) over a p-adic field

Let $F$ be a finite extension of ${\mathbb{Q}} \_p$. Any dihedral supercuspidal representation of $GL \_2 (K)$ arises from an admissible multiplicative character $ω$ of a quadratic extension $L$ of $K$. We show that such a representation is distinguished for $GL \_2 (F)$ if and only if $L$ biquadratic over $F$ and $ω$ restricted to invertibles of one of the two other quadratic extensions of $F$ in $L$ is trivial. We then observe a similar statement for the principal series and we study all dihedral representations.

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