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Symmetric and alternating powers of Weil representations of finite symplectic groups. (English) Zbl 07069218
Summary: 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.

MSC:
20C33 Representations of finite groups of Lie type
20C20 Modular representations and characters
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