On a question of Drinfeld on the Weil representation: The finite field case.

Let F be a finite field of odd cardinality, and let G = GL 2 ( F ) . The group G × G × G acts on F 2 ⊗ F 2 ⊗ F 2 via symplectic similitudes, and has a natural Weil representation. To answer a question raised by V. Drinfeld, we decompose that representation into irreducibles. We also decompose the analogous representation of GL 2 ( A ) , where A is a cubic algebra over F . [ABSTRACT FROM AUTHOR]