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This is a Quantitative Study study.

October 12, 2025Open Access

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

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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.

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This analysis determines irreducible representations of alternating and symmetric groups, highlighting unique eigenvalue characteristics.

Alexandre Zalesski (2025) studied this question.

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