Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1

2025/09/06 by Zalesski, Alexandre
#20B15 #20H30 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.05770

Abstract

We determine the irreducible representations of alternating and symmetric groups and their universal central extensions that contain a non-scalar element with all but one eigenvalues of multiplicity 1. The ground field is algebraically closed of arbitrary characteristic.

Citations

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

Related

• Cyclic Characters of Alternating Groups
• Spectra of non-regular elements in irreducible representations of simple algebraic groups
• Representations of symmetric and alternating groups and their double covers that remain irreducible modulo every prime
• Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups
• A multiplicity one theorem for groups of type A_n over discrete valuation rings