G(2)-Calogero-Moser Lax operators from reduction
Abstract
We construct a Lax operator for the
G
2
-Calogero-Moser model by means of a double reduction procedure. In the first reduction step we reduce the
A
6
-model to a
B
3
-model with the help of an embedding of the
B
3
-root system into the
A
6
-root system together with the specification of certain coupling constants. The
G
2
-Lax operator is obtained thereafter by means of an additional reduction by exploiting the embedding of the
G
2
-system into the
B
3
-system. The degree of algebraically independent and non-vanishing charges is found to be equal to the degrees of the corresponding Lie algebra.