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Orbital integrals on $\text{GL}_n \times \text{GL}_n \backslash \text{GL}_{2n}$

Part of: Lie groups

Published online by Cambridge University Press:  26 February 2021

Hang Xue
Hang Xue*
Affiliation:
Department of Mathematics, The University of Arizona, Tucson, AZ 85721, USA
*
e-mail: xuehang@math.arizona.edu
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Abstract

We study harmonic analysis on the symmetric space $\text{GL}_n \times \text{GL}_n \backslash \text{GL}_{2n}$. 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.

Keywords

orbital integralspherical characterssymmetric spaces

MSC classification

Primary: 22E35: Analysis on $p$-adic Lie groups

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 3 , June 2022 , pp. 858 - 886
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

This work is partially supported by the NSF grant DMS #1901862.

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