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Symmetric and alternating powers of Weil representations of finite symplectic groups
by Robert M. Guralnick   Kay Magaard   Pham Huu Tiep

Vol. 13 No. 4 (2018) P.443~P.461
 DOI: https://doi.org/10.21915/BIMAS.2018405 10.21915/BIMAS.2018405

ABSTRACT

Motivated by an earlier result of N. Katz, we establish all possible equalities between symmetric squares, alternating squares, and tensor products of complex irreducible Weil characters of finite symplectic groups in odd characteristic. We also construct an infinite series of examples of irreducible symmetric cubes and alternating cubes of complex representations of finite groups.

KEYWORDS
Finite symplectic groups, Weil representations.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20C33, 20C20.

MILESTONES