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.

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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