What question did this study set out to answer?

This research aims to explore the geometric properties of root systems through their orthogonal projections to a plane.

February 28, 2026

Orthogonal Projections of Root Systems to a Plane

Key Points

This research aims to explore the geometric properties of root systems through their orthogonal projections to a plane.
Analyzing type of root systems with specific simple roots
Examining the span of certain vectors in relation to the root systems
Deriving the properties of orthogonal projection vectors to identify inverse root systems
The set of nonzero orthogonal projection vectors forms the inverse root system of the analyzed root systems
This establishes new relationships between different types of root systems

Abstract

Consider the type Formula: see text root system with simple roots Formula: see text, and let Formula: see text be the span of Formula: see text and Formula: see text over Formula: see text. Let Formula: see text be any irreducible reduced root system but not of type Formula: see text, with rank Formula: see text. Namely, Formula: see text is of type Formula: see text (Formula: see text), Formula: see text (Formula: see text), Formula: see text (Formula: see text), Formula: see text, Formula: see text, Formula: see text or Formula: see text. We show that the set of nonzero orthogonal projection vectors of Formula: see text to the plane Formula: see text forms the inverse root system of Formula: see text.

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Cite This Study

Yongzhi Luan (Fri,) studied this question.

synapsesocial.com/papers/69a288170a974eb0d3c04076 https://doi.org/https://doi.org/10.1142/s1005386726000027

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