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PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS

Part of: Lie algebras and Lie superalgebras Global differential geometry

Published online by Cambridge University Press:  30 April 2019

JOHN M. BURNS  and
MOHAMMAD A. MAKROONI
JOHN M. BURNS
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland e-mails: mohammadadib.makrooni@nuigalway.ie, john.burns@nuigalway.ie
MOHAMMAD A. MAKROONI
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland e-mails: mohammadadib.makrooni@nuigalway.ie, john.burns@nuigalway.ie
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Abstract

In this note we consider parabolic subroot systems of a complex simple Lie Algebra. We describe root theoretic data of the subroot systems in terms of that of the root system and we give a selection of applications of our results to the study of generalized flag manifolds.

MSC classification

Primary: 53C30: Homogeneous manifolds
Secondary: 17B20: Simple, semisimple, reductive (super)algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 2 , May 2020 , pp. 355 - 366
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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