Automorphic tensor products and cuspidal cohomology of the \rm GL₄

2021/11/10 by Chandrasheel Bhagwat, Bhagwat, Chandrasheel, Sudipa Mondal +1
Mathematics · #11F41 #11F75 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.05753

openalex publication_date 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we establish an asymptotic lower bound estimate on the contribution of cuspidal automorphic representations of \rm GL₄(\mathbb A_{\mathbb Q}) to cuspidal cohomology of the \rm GL₄ which are obtained from automorphic tensor product of two automorphic representations of \rm GL₂(\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 GL₂ and the automorphic tensor product of two representations of \rm GL₂ can not be equal (up to a twist by a character of \rm GL₁) to each other, under the suitable assumptions on the representations being cuspidal and cohomological.

Citations

• Algebraic cycles on Hilbert modular fourfolds and poles of L-functions
• Cuspidality of symmetric powers with applications

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• Cuspidal cohomology classes for GL_n(Z)