What question did this study set out to answer?

The aim is to compute the restriction of a 23-dimensional character of the Mathieu group M24 to an S3 subgroup.

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April 5, 2026Open Access

S3 restriction of the deleted permutation character of the Mathieu group M24

Key Points

The aim is to compute the restriction of a 23-dimensional character of the Mathieu group M24 to an S3 subgroup.
Computed character restrictions from M24 to S3 subgroup
Analyzed decomposition into trivial and non-trivial components
Used GAP and Python for computational verification
Decomposition: 9 trivial, 2 sign, 6 standard representations
Engine values identified: S2r(3A) = 9, chi(5A) - 1 = 2, fix(3A) = 6
Noncanonical 5-dimensional subrepresentation provides symmetric power values of 1, 3, 7, 13, 22, 34

Abstract

We compute the restriction of the 23-dimensional deleted permutation character of M24 to an S3 subgroup whose transposition and 3-cycle lie in conjugacy classes 2A and 3A respectively. The decomposition is 9 trivial + 2 sign + 6 standard. All three multiplicities are engine values: S2r(3A) = 9, chi(5A) - 1 = 2, and fix(3A) = 6. A noncanonical 5-dimensional subrepresentation yields symmetric power values 1, 3, 7, 13, 22, 34 at a transposition, providing a natural S3 shadow compatible with Kähler geometry frameworks using dim(V) = 5. All results were verified computationally in GAP and Python.

S3 restriction of the deleted permutation character of the Mathieu group M24

Key Points

Abstract

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