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 1 is not an eigenvalue of theta(g). We also give estimates of the asymptotic behaviour of eigenvalue multiplicities when the rank of H grows and s is fixed.

DI MARTINO, L., Zalesski, A. (2008). Eigenvalues of unipotent elements in cross-characteristic representations of finite classical groups. JOURNAL OF ALGEBRA, 319(7), 2668-2722 [10.1016/j.jalgebra.2007.12.024].

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

DI MARTINO, LINO GIUSEPPE;
2008

Abstract

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 1 is not an eigenvalue of theta(g). We also give estimates of the asymptotic behaviour of eigenvalue multiplicities when the rank of H grows and s is fixed.
Articolo in rivista - Articolo scientifico
cross charactersitic representations of classical groups, minimum polynomials and spectra of unipotent elements, asymptotic estimates of eigenvalue multiplicities
English
2008
319
7
2668
2722
none
DI MARTINO, L., Zalesski, A. (2008). Eigenvalues of unipotent elements in cross-characteristic representations of finite classical groups. JOURNAL OF ALGEBRA, 319(7), 2668-2722 [10.1016/j.jalgebra.2007.12.024].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/2262
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