Strings in abstract root systems

2024/12/15 by Sanmartin-Lopez, Victor
#Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2412.11219

Abstract

Let Φ be a subset of the simple roots of a (possibly non-reduced) abstract root system Σ, and let λ∈ Σ. We define the Φ-string of λ as the set of elements in Σ∪ \0\ of the form λ+ ∑_{α∈ Φ} n_αα, where n_α is an integer for each α∈ Φ. This notion can be regarded as some sort of generalization of the classical notion of α-string, where α∈ Σ.

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