On intertwining numbers
type: Item
instance of: scholarly article
title: On intertwining numbers
zbMATH Open document ID: 0841.16017
author: Delia Flores de Chela
published in: Journal of Algebra
publication date: 1996-06-02T00:00:00Z
review text: 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.
reviewed by: Daniel Krob
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 735320
zbMATH Keywords: partitions
zbMATH Keywords: Schur algebras
zbMATH Keywords: Weyl modules
zbMATH Keywords: explicit formula
zbMATH Keywords: intertwining numbers
MaRDI profile type: Publication
full work available at URL: jabr.1995.1031
OpenAlex ID: W2089650022
DOI: 10.1006/JABR.1995.1031
description: scientific article; zbMATH DE number 735320