Cross characteristic representations of even characteristic symplectic groups

Guralnick, Robert; Tiep, Pham

doi:10.1090/S0002-9947-04-03477-4

Cross characteristic representations of even characteristic symplectic groups
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by Robert M. Guralnick and Pham Huu Tiep PDF

Trans. Amer. Math. Soc. 356 (2004), 4969-5023 Request permission

Abstract:

We classify the small irreducible representations of $Sp_{2n}(q)$ with $q$ even in odd characteristic. This improves even the known results for complex representations. The smallest representation for this group is much larger than in the case when $q$ is odd. This makes the problem much more difficult.

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