On special covariants in the exterior algebra of a simple Lie algebra
type: Item
instance of: scholarly article
title: On special covariants in the exterior algebra of a simple Lie algebra
zbMATH Open document ID: 1318.17006
DOI: 10.4171/RLM/682
author: Pierluigi Möseneder Frajria
author: Paolo Papi
author: Corrado De Concini
author: Claudio Procesi
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2014-11-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1404.4222
review text: Summary: We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the \(n\)-th symmetric power of the defining representation. As main result we prove that this subspace is a free module over the subalgebra of the exterior algebra generated by all primitive invariants except the one of highest degree.
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 6363542
zbMATH Keywords: exterior algebra
zbMATH Keywords: invariants
zbMATH Keywords: little adjoint representation
zbMATH Keywords: small representation
Wikidata QID: Q115211937
MaRDI profile type: Publication
arXiv ID: 1404.4222
cites work: Graded multiplicities in the exterior algebra
cites work: The sum of generalized exponents and Chevalley's restriction theorem for modules of covariants
cites work: Lie Group Representations on Polynomial Rings
cites work: Q675876
cites work: Invariant theory of little adjoint modules
cites work: Exterior Powers of the Adjoint Representation
cites work: First Layer Formulas for Characters of SL(n, C)
OpenAlex ID: W2017578229
description: scientific article; zbMATH DE number 6363542