G(2)-Calogero-Moser Lax operators from reduction

Details G(2)-Calogero-Moser Lax operators from reduction G(2)-Calogero-Moser Lax operators from reduction

2005-10-03

arxiv.org/abs/hep-th/0510012v1

J.Nonlin.MathematicalPhys.13:467-478,2006

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Latex

Scientific paper

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.

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