G2-Calogero-Moser lax operators from reduction

Abstract

We construct a Lax operator for the G2-Calogero-Moser model by means of a double reduction procedure. In the first reduction step we reduce the A6-model to a B3-model with the help of an embedding of the B3-root system into the A6-root system together with the specification of certain coupling constants. The G2-Lax operator is obtained thereafter by means of an additional reduction by exploiting the embedding of the G2-system into the B3-system. The degree of algebraically independent and non-vanishing charges is found to be equal to the degrees of the corresponding Lie algebra.