Some remarks on branching rules and tensor products for algebraic groups
type: Item
instance of: scholarly article
title: Some remarks on branching rules and tensor products for algebraic groups
zbMATH Open document ID: 0974.20031
author: Jonathan Brundan
author: Alexander S. Kleshchev
published in: Journal of Algebra
publication date: 2001-09-05T00:00:00Z
review text: Let \(\mathbb{F}\) be an algebraically closed field of characteristic \(p>0\). If \(L\) is some irreducible rational \(\text{GL}_n(\mathbb{F})\)-module and \(V\) is the natural \(\text{GL}_n(\mathbb{F})\)-module, there is a close relationship between the highest weight vectors (relative to \(\text{GL}_{n-1}(\mathbb{F})\)) in the restriction \(L \downarrow_{\text{GL}_{n-1}(\mathbb{F})}\) and the highest weight vectors (relative to \(\text{GL}_n(\mathbb{F})\)) in the tensor product \(L\otimes V^*\). The authors obtain more results on various relations between the branching rules from \(\text{GL}_n(\mathbb{F})\) to its Levi subgroups and on decompositions of tensor products over \(\text{GL}_n(\mathbb{F})\) itself. Some of these results are valid for arbitrary type.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1340616
zbMATH Keywords: tensor products
zbMATH Keywords: algebraic groups
zbMATH Keywords: irreducible modules
zbMATH Keywords: highest weight vectors
zbMATH Keywords: branching rules
MaRDI profile type: Publication
OpenAlex ID: W2137712186
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DOI: 10.1006/JABR.1998.7813
description: scientific article; zbMATH DE number 1340616