A Question on Splitting of Metaplectic Covers

Shiv Prakash Patel

doi:10.1080/00927872.2016.1147570

A Question on Splitting of Metaplectic Covers

Shiv Prakash Patel

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

1 Scopus citations

Abstract

Let F be a non-Archimedian local field. Splitting of twofold metaplectic cover of Sp_2n(F) restricted to various subgroups of Sp_2n(F) is important in application of the Weil representation of the metaplectic group. Let E/F be a quadratic extension. In this paper, we prove the splitting of the metaplectic cover of GL₂(E) restricted to the subgroup D_F^x , where D_F is the quaternion division algebra with center F, as a first step in our study of the restriction of representations of metaplectic cover of GL₂(E) to GL₂(F) and D_F^x. These results were suggested to the author by Professor Dipendra Prasad.

Original language	English
Pages (from-to)	5095-5104
Number of pages	10
Journal	Communications in Algebra
Volume	44
Issue number	12
DOIs	https://doi.org/10.1080/00927872.2016.1147570
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Quaternion division algebra
Splitting of metaplectic covers

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927872.2016.1147570

Cite this

@article{d366450c40a4476c92fbb31584f40282,

title = "A Question on Splitting of Metaplectic Covers",

abstract = "Let F be a non-Archimedian local field. Splitting of twofold metaplectic cover of Sp2n(F) restricted to various subgroups of Sp2n(F) is important in application of the Weil representation of the metaplectic group. Let E/F be a quadratic extension. In this paper, we prove the splitting of the metaplectic cover of GL2(E) restricted to the subgroup DFx , where DF is the quaternion division algebra with center F, as a first step in our study of the restriction of representations of metaplectic cover of GL2(E) to GL2(F) and DFx. These results were suggested to the author by Professor Dipendra Prasad.",

keywords = "Quaternion division algebra, Splitting of metaplectic covers",

author = "Patel, \{Shiv Prakash\}",

note = "Publisher Copyright: {\textcopyright} 2016, Copyright {\textcopyright} Taylor \& Francis Group, LLC.",

year = "2016",

month = dec,

day = "1",

doi = "10.1080/00927872.2016.1147570",

language = "English",

volume = "44",

pages = "5095--5104",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "12",

}

TY - JOUR

T1 - A Question on Splitting of Metaplectic Covers

AU - Patel, Shiv Prakash

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let F be a non-Archimedian local field. Splitting of twofold metaplectic cover of Sp2n(F) restricted to various subgroups of Sp2n(F) is important in application of the Weil representation of the metaplectic group. Let E/F be a quadratic extension. In this paper, we prove the splitting of the metaplectic cover of GL2(E) restricted to the subgroup DFx , where DF is the quaternion division algebra with center F, as a first step in our study of the restriction of representations of metaplectic cover of GL2(E) to GL2(F) and DFx. These results were suggested to the author by Professor Dipendra Prasad.

AB - Let F be a non-Archimedian local field. Splitting of twofold metaplectic cover of Sp2n(F) restricted to various subgroups of Sp2n(F) is important in application of the Weil representation of the metaplectic group. Let E/F be a quadratic extension. In this paper, we prove the splitting of the metaplectic cover of GL2(E) restricted to the subgroup DFx , where DF is the quaternion division algebra with center F, as a first step in our study of the restriction of representations of metaplectic cover of GL2(E) to GL2(F) and DFx. These results were suggested to the author by Professor Dipendra Prasad.

KW - Quaternion division algebra

KW - Splitting of metaplectic covers

UR - https://www.scopus.com/pages/publications/84979072565

U2 - 10.1080/00927872.2016.1147570

DO - 10.1080/00927872.2016.1147570

M3 - Article

AN - SCOPUS:84979072565

SN - 0092-7872

VL - 44

SP - 5095

EP - 5104

JO - Communications in Algebra

JF - Communications in Algebra

IS - 12

ER -

A Question on Splitting of Metaplectic Covers

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this