Relating homomorphism spaces between Specht modules of different degrees

2021/08/12 by Maliakas, Mihalis, Stergiopoulou, Dimitra-Dionysia
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2108.05733

Abstract

Let K be an infinite field of characteristic p>0 and let λ, μ be partitions of n, where λ=(λ₁,...,λ_n) and μ=(μ₁,..,μ_n). By S^λ we denote the Specht module corresponding to λ for the group algebra K\mathfrakS_n of the symmetric group \mathfrakS_n. D. Hemmer has raised the question of relating the homomorphism spaces \Hom_\mathfrakS_n(S^μ, S^λ) and \Hom_\mathfrakS_n'(S^μ+, S^λ+), where n'=n+kp^d, λ⁺ =λ+(kp^d), μ⁺=μ+(kp^d), and d, k are positive integers. We show that these are isomorphic if p is odd, p^d >min\λ₂, μ₁-λ₁\ and μ₂ ≤ λ₁.

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