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

2025/12/16 by S. Velmurugan, S, Velmurugan
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2512.14381

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 ≤ S_n. Analogous results are obtained for the alternating group A_n.

Citations

• Fixed Point Free Actions of Group Elements in Linear Groups and Finite Group Representations
• On eigenvalues of permutations in irreducible representations of symmetric and alternating groups
• On Minimal Polynomials of Elements in Symmetric and Alternating Groups
• The McKay Conjecture on character degrees
• Cyclic Characters of Alternating Groups
• On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups
• Sylow branching coefficients and hook partitions
• The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups
• On the Existence of Tableaux with Given Modular Major Index
• On conjugacy classes of S_n containing all irreducibles

Related

• Positivity of Sylow branching coefficients of symmetric groups
• On plethysms and Sylow branching coefficients
• Branching rules for the Weyl Groups of the Unitary and Orthogonal Lie\n Groups
• Sylow branching trees for symmetric groups
• Reduction for branching multiplicities