Coxeter exponents and orthogonal complements of highest roots

John Michael Burns

doi:10.1080/00927872.2020.1723020

Coxeter exponents and orthogonal complements of highest roots

John Michael Burns

Mathematics

University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

Abstract

In this note, we study the subroot system of an irreducible (reduced, crystallographic) root system obtained by taking the orthogonal complement of the highest root. We describe root theoretic data (the Coxeter number and the largest coefficient of the highest root when expressed in terms of the simple roots) of this subroot system in terms of that of As an application, we obtain a new description of the Coxeter exponents of a complex simple Lie algebra.

Original language	English (Ireland)
Pages (from-to)	2833-2843
Number of pages	11
Journal	Communications In Algebra
Volume	48
Issue number	7
DOIs	https://doi.org/10.1080/00927872.2020.1723020
Publication status	Published - 1 Feb 2020

Keywords

Coxeter exponent
Wolf space
subroot system

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Burns, JM,Makrooni, MA

Access to Document

10.1080/00927872.2020.1723020

Cite this

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title = "Coxeter exponents and orthogonal complements of highest roots",

abstract = "In this note, we study the subroot system of an irreducible (reduced, crystallographic) root system obtained by taking the orthogonal complement of the highest root. We describe root theoretic data (the Coxeter number and the largest coefficient of the highest root when expressed in terms of the simple roots) of this subroot system in terms of that of As an application, we obtain a new description of the Coxeter exponents of a complex simple Lie algebra.",

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AB - In this note, we study the subroot system of an irreducible (reduced, crystallographic) root system obtained by taking the orthogonal complement of the highest root. We describe root theoretic data (the Coxeter number and the largest coefficient of the highest root when expressed in terms of the simple roots) of this subroot system in terms of that of As an application, we obtain a new description of the Coxeter exponents of a complex simple Lie algebra.

KW - Coxeter exponent

KW - Wolf space

KW - subroot system

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DO - 10.1080/00927872.2020.1723020

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JO - Communications In Algebra

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ER -

Coxeter exponents and orthogonal complements of highest roots

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

Access to Document

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