On intertwining numbers
Let \(\lambda=(\lambda_1,\dots,\lambda_k)\) be a partition and let \(d\), \(i\), \(j\) be positive integers such that \[ \mu=\mu(d,i,j)=(\lambda_1,\dots,\lambda_i+d,\dots,\lambda_j-d,\dots,\lambda_l) \] is still a partition. Let then \(\overline{A}_s\) be the Schur algebra of degree \(s=|\lambda|\) over \(\mathbb{Z}/p\mathbb{Z}\) where \(p\) is a prime number and let \(\overline{K}_\lambda\) be the Weyl module of shape \(\lambda\) over \(\mathbb{Z}/p\mathbb{Z}\). This paper is devoted to the proof an explicit formula for the intertwining numbers \(\varepsilon_p(\lambda,d,i,j)=\dim\text{Hom }_{\overline{A}_s}(\overline{K}_\lambda,\overline{K}_\mu)\) that was proposed as a conjecture by Akin and Buchsbaum.
scientific article; zbMATH DE number 735320