Matrices of simple spectrum in irreducible representations of cyclic extensions of simple algebraic groups

2021/04/22 by Zalesski, Alexandre
#20C20 #20G05 #20G40 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2104.10882

Abstract

Let H be a linear algebraic group whose connected component G≠ 1 is simple and H/G is cyclic. We determine the irreducible projective representations ϕ of H such that ϕ(G) is irreducible and ϕ(h) has simple spectrum for some h∈ H. The latter means that all irreducible constituents of the group ϕ( ⟨ h⟩) are of multiplicity 1. (Here ⟨ h⟩ is the subgroup of H generated by h.) This extends an earlier known result for H=G.

Related

• Spectra of non-regular elements in irreducible representations of simple algebraic groups
• Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups
• Almost cyclic regular elements in irreducible representations of simple algebraic groups
• Irreducible subgroups of simple algebraic groups - a survey
• On generators and representations of the sporadic simple groups