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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… Click to show full abstract
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.
Keywords:
exponents orthogonal;
complements highest;
coxeter exponents;
orthogonal complements;
root;
coxeter
Journal Title: Communications in Algebra
Year Published: 2020
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Journal Title: Communications in Algebra
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!