Eigenvalues of unipotent elements in cross-characteristic representations of finite classical groups

JOURNAL OF ALGEBRA

卷:319

Article

Di Martino, L.¹  Zalesskii, A. E.² 

[1] Univ Studi Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[2] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

关键词: finite classical groups;    cross-characteristic representations;    unipotent elements;    eigenvalue multiplicities;   

DOI  :  10.1016/j.jalgebra.2007.12.024

来源: Elsevier

【 摘 要 】

Let H be a finite classical group, g be a unipotent element of H of order s and theta be an irreducible representation of H with dim theta > 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 theta(g), and classify all the triples (H, g, theta) for which this does not hold. In particular, we list the triples for which I is not an eigenvalue of (g). We also give estimates of the asymptotic behavior of eigenvalue multiplicities when the rank of H grows and s is fixed. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free