Automorphic tensor products and cuspidal cohomology of the ${\rm GL}_4$

Chandrasheel Bhagwat; Sudipa Mondal

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arXiv · 2111.05753

Automorphic tensor products and cuspidal cohomology of the ${\rm GL}_4$

Chandrasheel Bhagwat·Sudipa Mondal

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Abstract

In this article, we establish an asymptotic lower bound estimate on the contribution of cuspidal automorphic representations of ${\rm GL}_4(\mathbb A_{\mathbb Q})$ to cuspidal cohomology of the ${\rm GL}_4$ which are obtained from automorphic tensor product of two automorphic representations of ${\rm GL}_2(\mathbb A_{\mathbb Q})$ of given weights and with varying level structure. In the end, we also prove that the symmetric cube of a representation of ${\rm GL}_2$ and the automorphic tensor product of two representations of ${\rm GL}_2$ can not be equal (up to a twist by a character of ${\rm GL}_1$) to each other, under the suitable assumptions on the representations being cuspidal and cohomological.

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Chandrasheel Bhagwat, Sudipa Mondal. 2021-11-10. Automorphic tensor products and cuspidal cohomology of the ${\rm GL}_4$. https://arxiv.org/abs/2111.05753

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