Abstract
For all cusp forms π on GL(3) and π′ on GL(2) over a number field F, H. Kim and F. Shahidi have functorially associated an automorphic form Formula on GL(6) such that L(s, Π) agrees with the Rankin-Selberg L-function of the pair (π, π′). First we establish a criterion as to when Π is cuspidal. Then we apply it to construct non-self-dual, nonmonomial cuspidal cohomology classes for suitable congruence subgroups of SL(3, ℤ). We also analyze the Galois image of certain related l-adic representations.
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