Automorphic tensor products and cuspidal cohomology of the GL(4)

Abstract

In this paper, we establish an asymptotic lower bound estimate on the contribution of cuspidal automorphic representations of GL4(AQ)GL4(𝔸ℚ) to cuspidal cohomology of the GL4GL4 which are obtained from automorphic tensor product of two automorphic representations of GL2(AQ)GL2(𝔸ℚ) of given weights and with varying level structure. In the end, we also prove that the symmetric cube of a representation of GL2GL2 and the automorphic tensor product of two representations of GL2GL2 cannot be equal (up to a twist by a character of GL1GL1) to each other, under the suitable assumptions on the representations being cuspidal and cohomological