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This research aims to explore the eigenvalue linkage between the spin-½ and spin-3/2 representations of the binary icosahedral group 2I.

August 9, 2026Open Access

An Exact Laplacian-Eigenvalue Degeneracy Between the Spin-½ and Spin-3/2 Representations of 2I

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This research aims to explore the eigenvalue linkage between the spin-½ and spin-3/2 representations of the binary icosahedral group 2I.
Analyzed the Cayley-graph Laplacian of the binary icosahedral group 2I with a specified generating set.
Utilized Schur's lemma to evaluate the action on the four-dimensional character that represents the spin-3/2 sector.
Defined admissibility windows for both spin sectors using the spectral admissibility framework.
Both spin-½ and spin-3/2 representations yield the same Laplacian eigenvalue, λ = 18.
Their spectral admissibility windows are identical under the defined criteria A^{max}_ρ.
The findings emphasize that this degeneracy is purely a mathematical property, lacking physical selection implications.

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Randomized trial examines eigenvalue degeneracy in spin representations of 2I, suggesting foundational implications for group theory.

Jérôme Beau (2026) studied this question.

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