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$\text{GL}_n \times \text{GL}_n \backslash \text{GL}_{2n}$
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.
