# Rankin-Selberg convolutions for $\mathrm{GL}(n)\times \mathrm{GL}(n)$ and $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ for principal series representations

@inproceedings{Liu2021RankinSelbergCF, title={Rankin-Selberg convolutions for \$\mathrm\{GL\}(n)\times \mathrm\{GL\}(n)\$ and \$\mathrm\{GL\}(n)\times \mathrm\{GL\}(n-1)\$ for principal series representations}, author={Dongwen Liu and Fengqiu Su and Binyong Sun}, year={2021} }

Let k be a local field. Let Iν and Iν′ be smooth principal series representations of GLn(k) and GLn−1(k) respectively. The Rankin-Selberg integrals yield a continuous bilinear map Iν × Iν′ → C with a certain invariance property. We study integrals over a certain open orbit that also yield a continuous bilinear map Iν × Iν′ → C with the same invariance property, and show that these integrals equal the Rankin-Selberg integrals up to an explicit constant. Similar results are also obtained for… Expand

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