Criteria for the existence of cuspidal theta representations

Solomon Friedberg; David Ginzburg

doi:https://doi.org/10.1007/s40993-016-0046-6

Criteria for the existence of cuspidal theta representations

Solomon Friedberg, David Ginzburg

School of Mathematical Sciences

Tel Aviv University

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

Abstract

Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal theta representation is one which is equal to the local twisted theta representation at almost all places. Cuspidal theta representations are known to exist but only for covers of GL_j, j≤ 3. In this paper we establish necessary conditions for the existence of cuspidal theta representations on the r-fold metaplectic cover of the general linear group of arbitrary rank.

Original language	English
Article number	16
Journal	Research in Number Theory
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/s40993-016-0046-6
State	Published - 1 Dec 2016

Keywords

Cuspidal theta representation
Eisenstein series
Metaplectic group
Residual representation
Theta representation
Unipotent orbit

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1007/s40993-016-0046-6

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abstract = "Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal theta representation is one which is equal to the local twisted theta representation at almost all places. Cuspidal theta representations are known to exist but only for covers of GLj, j≤ 3. In this paper we establish necessary conditions for the existence of cuspidal theta representations on the r-fold metaplectic cover of the general linear group of arbitrary rank.",

keywords = "Cuspidal theta representation, Eisenstein series, Metaplectic group, Residual representation, Theta representation, Unipotent orbit",

author = "Solomon Friedberg and David Ginzburg",

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T1 - Criteria for the existence of cuspidal theta representations

AU - Friedberg, Solomon

AU - Ginzburg, David

PY - 2016/12/1

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N2 - Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal theta representation is one which is equal to the local twisted theta representation at almost all places. Cuspidal theta representations are known to exist but only for covers of GLj, j≤ 3. In this paper we establish necessary conditions for the existence of cuspidal theta representations on the r-fold metaplectic cover of the general linear group of arbitrary rank.

AB - Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal theta representation is one which is equal to the local twisted theta representation at almost all places. Cuspidal theta representations are known to exist but only for covers of GLj, j≤ 3. In this paper we establish necessary conditions for the existence of cuspidal theta representations on the r-fold metaplectic cover of the general linear group of arbitrary rank.

KW - Cuspidal theta representation

KW - Eisenstein series

KW - Metaplectic group

KW - Residual representation

KW - Theta representation

KW - Unipotent orbit

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DO - https://doi.org/10.1007/s40993-016-0046-6

M3 - مقالة

SN - 2363-9555

VL - 2

JO - Research in Number Theory

JF - Research in Number Theory

IS - 1

M1 - 16

ER -

Criteria for the existence of cuspidal theta representations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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