Orbital integrals on GLn× GLn/GL2n

Hang Xue

doi:10.4153/S0008414X21000122

Orbital integrals on GL_n× GL_n/GL_2n

Hang Xue

Mathematics

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

2 Scopus citations

Abstract

We study harmonic analysis on the symmetric space GL_n× GL_n/GL_2n We prove several standard results, e.g. Shalika germ expansion of orbital integrals, representability of the Fourier transform of orbital integrals and representability of spherical characters. These properties are not expected to hold for symmetric spaces in general.

Original language	English (US)
Pages (from-to)	858-886
Number of pages	29
Journal	Canadian Journal of Mathematics
Volume	74
Issue number	3
DOIs	https://doi.org/10.4153/S0008414X21000122
State	Published - Jun 26 2022

Keywords

orbital integral
spherical characters
symmetric spaces

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4153/S0008414X21000122

Cite this

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title = "Orbital integrals on GLn× GLn/GL2n",

abstract = "We study harmonic analysis on the symmetric space GLn× GLn/GL2n We prove several standard results, e.g. Shalika germ expansion of orbital integrals, representability of the Fourier transform of orbital integrals and representability of spherical characters. These properties are not expected to hold for symmetric spaces in general.",

keywords = "orbital integral, spherical characters, symmetric spaces",

author = "Hang Xue",

note = "Publisher Copyright: {\textcopyright} Canadian Mathematical Society 2021.",

year = "2022",

month = jun,

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N2 - We study harmonic analysis on the symmetric space GLn× GLn/GL2n We prove several standard results, e.g. Shalika germ expansion of orbital integrals, representability of the Fourier transform of orbital integrals and representability of spherical characters. These properties are not expected to hold for symmetric spaces in general.

AB - We study harmonic analysis on the symmetric space GLn× GLn/GL2n We prove several standard results, e.g. Shalika germ expansion of orbital integrals, representability of the Fourier transform of orbital integrals and representability of spherical characters. These properties are not expected to hold for symmetric spaces in general.

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KW - spherical characters

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