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

Key Points

• The study identifies irreducible representations of alternating and symmetric groups with specific eigenvalue multiplicities.
• All but one eigenvalue of multiplicity 1 are found in representations tying to non-scalar elements.
• The ground field considered is algebraically closed, promoting diverse characteristics of the studied groups.
• Universal central extensions of these groups are explored within the framework of their eigenvalues.