Tensor Products of Weil Modules

The aim of this work is to understand the decomposition, in irreducible modules, of tensor products of Weil modules for Sp2n(3). To do this, we begin by computing the Weil modules for Sp4(3), Sp6(3) and Sp8(3) in order to understand how tensor products decompose for these cases. This leads us to some results and hypotheses for the general case. The understanding of the decomposition of two-fold tensor product of Weil modules for Sp2n(3) has been treated by Kay Magaard and Pham Huu Tiep in “Irreducible tensor products of representations of finite quasi-simple groups of Lie type” (to appear in the Proceedings of the Virginia Symposium on Representations of Finite Groups). Following it, we try to understand as much as possible the decomposition of three-fold tensor products of Weil modules for Sp2n(3).