Skew Schur polynomials and cyclic sieving phenomenon

2021/12/23 by So Yeon Lee, Lee, So-Yeon, Young-Tak Oh +1
Mathematics · #05E05 #05E10 #05E18 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2112.12394

openalex publication_date 2021/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k and m be positive integers and λ/μ a skew partition. We compute the principal specialization of the skew Schur polynomials s_λ/μ(x₁, …, x_k) modulo q^m-1 under suitable conditions. We interpret the results thus obtained from the viewpoint of the cyclic sieving phenomenon on semistandard Young skew tableaux of shape λ/μ. As an application, we deal with evaluations of the principal specialization of the skew Schur polynomials at roots of unity.

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