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The study investigates the internal structures of the 2-Sylow subgroup of S6 to uncover algebraic relationships leading to the Standard Model.

April 12, 2026Open Access

Internal structure of the S₆ vacuum: from Pauli matrices to the Standard Model gauge algebra

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Analysis identifies complex algebraic structures in S6 vacuum, suggesting new insights for gauge symmetry.

The study investigates the internal structures of the 2-Sylow subgroup of S6 to uncover algebraic relationships leading to the Standard Model.
Analyzed the representation of Pauli matrices within the subgroup's structure.
Characterized involution pairs and active differences using trace properties.
Examined fermionic families and parity relations in relation to gauge invariance.
Classified transpositions into distinct patterns for block structure analysis.
Constructed the gauge algebra representation explicitly and verified findings computationally.
Identified 1200 involution pairs linked to specific subgroup classifications.
Demonstrated the emergence of sl(3, C)⊕sl(2, C)⊕u(1) in the gauge algebra.
Showed a correspondence between symmetry breaking chains and algebraic structures.
Established that the properties derived hold for independent computations.

Davide Cirillo (2026) studied this question.

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