On homomorphisms indexed by semistandard tableaux

2011/01/17 by Sinéad Lyle, Sinead Lyle, Lyle, Sinead · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1101.3192

32 pages. This third version of the paper contains some comments on homomorphisms between the Specht modules defined by Dipper and James and has a more rigorous proof of the result following Proposition 4.1

openalex publication_date 2011/01/17 · arxiv created 2011/09/09 · arxiv updated 2011/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the homomorphism spaces between Specht modules for the Hecke algebras \h of type A. We prove a cellular analogue of the kernel intersection theorem and a q-analogue of a theorem of Fayers and Martin and apply these results to give an algorithm which computes the homomorphism spaces \Hom_\h(S^μ,S^λ) for certain pairs of partitions λ and μ. We give an explicit description of the homomorphism spaces \Hom_\h(S^μ,S^λ) where \h is an algebra over the complex numbers, λ=(λ₁,λ₂) and μ is an arbitrary partition with μ₁ ≥ λ₂.

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