A kernel formula for the action of the Weyl element in the Kirillov model of SL(2,C)

Ehud Moshe Baruch; Orr Beit-Aharon

doi:10.1016/j.jnt.2014.02.001

A kernel formula for the action of the Weyl element in the Kirillov model of SL(2,C)

Ehud Moshe Baruch, Orr Beit-Aharon

Mathematics

Technion - Israel Institute of Technology

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

Abstract

We give an explicit description of the action of the Weyl element on smooth functions with compact support in the Kirillov model of non-principal series irreducible representations of SL(2,C) generalizing a result of Motohashi. An important ingredient in the proof of the kernel formula is a new "classical" formula for an integral involving Bessel functions. We also give an analogous formula for GL(2,C).

Original language	English
Pages (from-to)	23-40
Number of pages	18
Journal	Journal of Number Theory
Volume	146
Issue number	C
DOIs	https://doi.org/10.1016/j.jnt.2014.02.001
State	Published - 2015

Keywords

Bessel functions
Kirillov model
Primary
Secondary

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2014.02.001

Cite this

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AU - Baruch, Ehud Moshe

AU - Beit-Aharon, Orr

PY - 2015

Y1 - 2015

N2 - We give an explicit description of the action of the Weyl element on smooth functions with compact support in the Kirillov model of non-principal series irreducible representations of SL(2,C) generalizing a result of Motohashi. An important ingredient in the proof of the kernel formula is a new "classical" formula for an integral involving Bessel functions. We also give an analogous formula for GL(2,C).

AB - We give an explicit description of the action of the Weyl element on smooth functions with compact support in the Kirillov model of non-principal series irreducible representations of SL(2,C) generalizing a result of Motohashi. An important ingredient in the proof of the kernel formula is a new "classical" formula for an integral involving Bessel functions. We also give an analogous formula for GL(2,C).

KW - Bessel functions

KW - Kirillov model

KW - Primary

KW - Secondary

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U2 - 10.1016/j.jnt.2014.02.001

DO - 10.1016/j.jnt.2014.02.001

M3 - مقالة

SN - 0022-314X

VL - 146

SP - 23

EP - 40

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - C

ER -

A kernel formula for the action of the Weyl element in the Kirillov model of SL(2,C)

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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