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.

12 pages, Latex

References in corpus (1)

• Non-crystallographic reduction of generalized Calogero-Moser models

Cited by in corpus (4)

• PT-symmetric deformations of Calogero models
• Antilinear deformations of Coxeter groups, an application to Calogero models
• Higher derivative Hamiltonians with benign ghosts from affine Toda lattices
• Intertwining operator for $A{G}_2$ Calogero-Moser-Sutherland system