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arXiv · 2512.14381

On the Positivity of Dihedral Branching Coefficients of the Symmetric and Alternating Groups

Velmurugan S
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Abstract

We determine precisely when the branching coefficients arising from the restriction of irreducible representations of the symmetric group $S_n$ to the dihedral subgroup $D_n$ are nonzero, and we establish uniform linear lower bounds outside a finite exceptional family. As a consequence, we recover and substantially generalize known positivity results for cyclic subgroups $C_n \leq S_n$. Analogous results are obtained for the alternating group $A_n$.

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Velmurugan S. 2025-12-16. On the Positivity of Dihedral Branching Coefficients of the Symmetric and Alternating Groups. https://arxiv.org/abs/2512.14381

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