A cuspidality criterion for the functorial product on GL(2) x GL(3), with a cohomological application
Abstract
This paper was motivated by a question of Avner Ash, asking if it is possible to construct non-selfdual, non-monomial, cuspidal cohomology classes for suitable congruence subgroups \Gamma of SL(n,\Z). Such a construction, in special examples, has been known for some time for n=3; it is of course impossible for n=2. We show in this paper the existence of many such examples for n=6, which are primitive, by making use of the functorial product on GL(2) x GL(3), which was recently shown to be automorphic by Kim and Shahidi. We establish a general cuspidality criterion for this product, which is essential to the construction. We also show that there exist non-selfdual, monomial (cuspidal) classes for any n=2m > 3, and non-selfdual, non-monomial (but imprimitive) classes for n=4.
Keywords
Cite
@article{arxiv.math/0310163,
title = {A cuspidality criterion for the functorial product on GL(2) x GL(3), with a cohomological application},
author = {Dinakar Ramakrishnan and Song Wang},
journal= {arXiv preprint arXiv:math/0310163},
year = {2007}
}