Classification of marked elliptic root systems with nonreduced quotient

Abstract

Saito (Publ. RIMS 21 (1), 1985, 75–179) has introduced a class of root systems called elliptic root systems that lie in the real vector space with a metric whose signature is of type . He also classified the pair of elliptic root systems with one‐dimensional subspaces of the radical of , under the assumption that the quotient root system is reduced. Here, we classify the pairs where is nonreduced.