On homomorphisms between Weyl modules: The case of a column transposition

2024/11/12 by Charalampos Evangelou, Evangelou, Charalampos
Mathematics · #Algebraic and Geometric Analysis #Spectral Theory in Mathematical Physics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2411.08208

Abstract

Let G=GL_n(K) be the general linear group defined over an infinite field K of positive characteristic p and let Δ(λ) be the Weyl module of G which corresponds to a partition λ. In this paper we classify all homomorphisms Δ(λ) → Δ(μ) when λ=(a,b,1^d) and μ=(a+d,b), d>1. In particular, we show that Hom_G(Δ(λ),Δ(μ)) is nonzero if and only if p=2 and a is even. In this case, we show that the dimension of the homomorphism space is equal to 1 and we provide an explicit generator whose description depends on binary expansions of various integers. We also show that these generators in general are not compositions of Carter-Payne homomorphisms.

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