2003/10/11 by Dinakar Ramakrishnan, Song Wang, Ramakrishnan, Dinakar +1 · 2 citations
Mathematics · #11F70 #11F75 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT #msc:11F70 #msc:11F75
paper · pdf · doi:10.48550/arxiv.math/0310163
arxiv created 2003/10/11 · openalex publication_date 2003/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Γof 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.