Branching rules and Hodge cycles on certain abelian varieties. (English) Zbl 0654.14005
The first part of this paper is representation theoretic: an explicit formula computing the branching rules for representations of sl(N) is proved which allows one to compute by hand in examples which so far were accessible only via computers. - The second part of the paper is an application of this formula to computing invariants of the Hodge group action on the cohomology space of certain 10-dimensional abelian varieties; in particular the Hodge conjecture is checked for the abelian varieties in question.
Reviewer: A.Buium
MSC:
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 20G05 | Representation theory for linear algebraic groups |
| 14K99 | Abelian varieties and schemes |
| 14E22 | Ramification problems in algebraic geometry |
| 22E55 | Representations of Lie and linear algebraic groups over global fields and adèle rings |
