Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587742 | Journal of Algebra | 2008 | 55 Pages |
Abstract
Let H be a finite classical group, g be a unipotent element of H of order s and θ be an irreducible representation of H with dimθ>1 over an algebraically closed field of characteristic coprime to s. We show that almost always all the s-roots of unity occur as eigenvalues of θ(g), and classify all the triples (H,g,θ) for which this does not hold. In particular, we list the triples for which 1 is not an eigenvalue of θ(g). We also give estimates of the asymptotic behavior of eigenvalue multiplicities when the rank of H grows and s is fixed.
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Mathematics
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