The construction of trigonometric invariants for Weyl groups and the derivation of corresponding exactly solvable Sutherland models

Abstract

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The invariants of the basis can be used as coordinates in any cell of the coroot space and lead to an exactly solvable model of Sutherland type. We apply this construction to the $F_4$ case

13 pages, no figures, latex 2epsilon, corrected version

References in corpus (1)

• An exactly solvable model of the Calogero type for the icosahedral group

Cited by in corpus (6)

• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Solvability of the Hamiltonians related to exceptional root spaces: rational case
• Solvability of the $F_4$ Integrable System
• Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariable Polynomials. II. $E_7$ case
• Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials. III. $E_8$ case
• Solvability of $F_4$ quantum integrable systems