Year: 2026
Type: preprint
Abstract: Motivated by John Baez's question about seven exceptional coincidences among binomial coefficients, we construct seven exterior-power identities for representations of $A_5$. Their common symmetry comes from simplex edges and icosahedral vertices, axes, and faces, together with characters of stabilizers. We enumerate all ordered pairs of representation isomorphism classes in the prescribed dimensions. Apart from the pair of trivial actions, the permutation pair at $1540$ and the complex monomial pair at $7140$ are unique. At $3003$, Klein's twelve-point divisor gives a noncanonical intertwiner factored through polynomial division, differentiation, and residues.
Source: arXiv (Cornell University)
Authors: Lupercio, Ernesto, Shaydurova, Evgeniya
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2174268181
OpenAlex ID: W7216061723