On disjointness of linear models and degenerate Whittaker models

Eitan Sayag; Mahendra Kumar Verma

doi:10.1016/j.jnt.2019.04.003

On disjointness of linear models and degenerate Whittaker models

Eitan Sayag, Mahendra Kumar Verma

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

In this article we reprove and generalize a result of N. Matringe [12] concerning generic representations of GL_n(F) that admits a linear model with respect to a maximal Levi subgroup GL_p(F)×GL_q(F), where F is a non-archimedean field. He showed that in this case |p−q|≤1. We extend this result to the case where F is a finite field or a local field of characteristic different from 2. Further, we study non-generic representations of GL_n(F) and describe their possible linear models in terms of their rank r(π) (see Section 6). Our arguments are based on the method of Gelfand-Kazhdan and the theory of distribution and provide uniform proofs for finite, p-adic and archimedean fields.

Original language	American English
Pages (from-to)	56-82
Number of pages	27
Journal	Journal of Number Theory
Volume	207
DOIs	https://doi.org/10.1016/j.jnt.2019.04.003
State	Published - 1 Feb 2020

Keywords

Degenerate Whittaker models
Disjointness
Linear models

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2019.04.003

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title = "On disjointness of linear models and degenerate Whittaker models",

abstract = "In this article we reprove and generalize a result of N. Matringe [12] concerning generic representations of GLn(F) that admits a linear model with respect to a maximal Levi subgroup GLp(F)×GLq(F), where F is a non-archimedean field. He showed that in this case |p−q|≤1. We extend this result to the case where F is a finite field or a local field of characteristic different from 2. Further, we study non-generic representations of GLn(F) and describe their possible linear models in terms of their rank r(π) (see Section 6). Our arguments are based on the method of Gelfand-Kazhdan and the theory of distribution and provide uniform proofs for finite, p-adic and archimedean fields.",

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T1 - On disjointness of linear models and degenerate Whittaker models

AU - Sayag, Eitan

AU - Verma, Mahendra Kumar

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N2 - In this article we reprove and generalize a result of N. Matringe [12] concerning generic representations of GLn(F) that admits a linear model with respect to a maximal Levi subgroup GLp(F)×GLq(F), where F is a non-archimedean field. He showed that in this case |p−q|≤1. We extend this result to the case where F is a finite field or a local field of characteristic different from 2. Further, we study non-generic representations of GLn(F) and describe their possible linear models in terms of their rank r(π) (see Section 6). Our arguments are based on the method of Gelfand-Kazhdan and the theory of distribution and provide uniform proofs for finite, p-adic and archimedean fields.

AB - In this article we reprove and generalize a result of N. Matringe [12] concerning generic representations of GLn(F) that admits a linear model with respect to a maximal Levi subgroup GLp(F)×GLq(F), where F is a non-archimedean field. He showed that in this case |p−q|≤1. We extend this result to the case where F is a finite field or a local field of characteristic different from 2. Further, we study non-generic representations of GLn(F) and describe their possible linear models in terms of their rank r(π) (see Section 6). Our arguments are based on the method of Gelfand-Kazhdan and the theory of distribution and provide uniform proofs for finite, p-adic and archimedean fields.

KW - Degenerate Whittaker models

KW - Disjointness

KW - Linear models

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DO - 10.1016/j.jnt.2019.04.003

M3 - Article

SN - 0022-314X

VL - 207

SP - 56

EP - 82

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

On disjointness of linear models and degenerate Whittaker models

Abstract

Keywords

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