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Computational analysis of character restrictions in Mathieu group M24 indicates implications for Kähler geometry.
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.
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Ronney Lyons (2026) studied this question.
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