On a question of Drinfeld on the Weil representation I: the finite field case
arXiv:1205.4859 · doi:10.1016/j.optcom.2012.10.047
Abstract
Let F be a finite field of odd cardinality, and let G= GL2(F). The group G \times G \times G acts on F^2 \otimes F^2 \otimes F^2 via symplectic similitudes, and has a natural Weil representation. Answering a question rasised by V. Drinfeld, we decompose that representation into irreducibles. We also decompose the analogous representation of GL2(A), where A is a cubic algebra over F.
29 pages. Comments welcome