On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups

2023/08/16 by P, Amrutha, Prasad, Amritanshu, S, Velmurugan · 3 citations
#05E10 #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2308.08146

Abstract

We determine when a permutation with cycle type μ admits a non-zero invariant vector in the irreducible representation V_λ of the symmetric group. We find that a majority of pairs (λ,μ) have this property, with only a few simple exceptions.

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