Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups

2023/02/03 by Alexandre Zalesski, Zalesski, Alexandre · 2 citations
Mathematics · #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2302.01824

Abstract

We study the irreducible representations of simple algebraic groups in which some non-central semisimple element has at most one eigenvalue of multiplicity greater than 1. We bound the multiplicity of this eigenvalue in terms of the rank of the group.

Cited by

• Fixed Point Free Actions of Group Elements in Linear Groups and Finite Group Representations
• Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1

Related

• Spectra of non-regular elements in irreducible representations of simple algebraic groups
• Matrices of simple spectrum in irreducible representations of cyclic extensions of simple algebraic groups
• Almost cyclic regular elements in irreducible representations of simple algebraic groups
• Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
• Cyclic Characters of Alternating Groups