Classification of marked elliptic root systems with non-reduced quotient

TL;DR

This paper extends Saito's classification of elliptic root systems by classifying pairs where the quotient root system is non-reduced, broadening understanding of these algebraic structures.

Contribution

It provides a classification of elliptic root systems with non-reduced quotients, which was not covered in prior classifications.

Findings

Classified pairs (R,G) with non-reduced quotient root systems.

Extended Saito's classification to a broader class of elliptic root systems.

Enhanced understanding of the structure of elliptic root systems.

Abstract

K. Saito (Publ. RIMS 21 (1), 1985, 75-179) has introduced a class of root systems called elliptic root systems which lies in the real vector space $F$ with a metric $I$ whose signature is of type $(l,2,0)$. He also classified the pair $(R,G)$ of an elliptic root system $R$ with one dimensional subspace $G$ of the radical of $I$, under the assumption that the quotient root system $R/G$ is reduced. Here, we classify the pairs $(R,G)$ where $R/G$ is non-reduced.