Geodesic
Orbital integrals on $\text{GL}_n \times \text{GL}_n \backslash \text{GL}_{2n}$
Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 858-886

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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.
DOI : 10.4153/S0008414X21000122
Mots-clés : orbital integral, spherical characters, symmetric spaces 
Xue, Hang. Orbital integrals on $\text{GL}_n \times \text{GL}_n \backslash \text{GL}_{2n}$. Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 858-886. doi: 10.4153/S0008414X21000122
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