Balanced subsets in root systems
Andrei Moroianu, Paul Schwahn
TL;DR
This paper investigates the sizes of well-balanced subsets within positive roots of compact Lie algebras, providing exact maximal and minimal sizes across all simple root systems.
Contribution
It computes the maximal and minimal sizes of well-balanced subsets in all simple root systems, advancing understanding in Lie algebra root structures.
Findings
Determined maximal sizes of well-balanced subsets in simple root systems.
Determined minimal sizes of well-balanced subsets in simple root systems.
Provides a comprehensive classification relevant to Hermitian and spin geometry.
Abstract
Balanced and well-balanced subsets of the set of positive roots of compact Lie algebras arise naturally in problems related to Hermitian and spin geometry. In this paper we compute the maximal and minimal size of well-balanced subsets in all simple root systems.
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