RECURRENCE RELATIONS AND DYNKIN DIAGRAMS

Abstract

In this note we give some applications of a recurrence relation between the vertex coefficients of the extended Dynkin diagram of a complex simple Lie algebra. In particular we derive a correspondence between the extended Dynkin diagrams (or infinite families of extended Dynkin diagrams ) of simply laced complex simple Lie algebras and the (infinite) subgroups G of P5L(2, C) that act discontinuously on C.