Classification of marked elliptic root systems with non-reduced affine quotient

Abstract

The class of root systems, called elliptic root systems, were introduced in 1985 by K. Saito, for his studies on a normal surface singularity which contains a regular elliptic curve in its minimal resolution. He also classified such root systems when they admit a reduced affine quotient, as root system. In this note, we provide the classification of elliptic root systems that admit a non-reduced affine quotient, thus complete the classification of such root systems.