Symmetric and alternating powers of Weil representations of finite symplectic groups
Robert M. Guralnick
Pham Huu Tiep
Vol. 13 No. 4 (2018) P.443~P.461
DOI: || https://doi.org/10.21915/BIMAS.2018405 |
| ||10.21915/BIMAS.2018405 |
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.
Finite symplectic groups, Weil representations.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20C33, 20C20.
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