Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariable Polynomials. II. $E_7$ case

Abstract

It is shown that the $E_7$ trigonometric Olshanetsky-Perelomov Hamiltonian, when written in terms of the Fundamental Trigonometric Invariants (FTI), is in algebraic form, i.e., has polynomial coefficients, and preserves the infinite flag of polynomial spaces with the characteristic vector $\vec{\alpha }=(1,2,2,2,3,3,4)$. Its flag coincides with one of the minimal characteristic vector for the $E_7$ rational model.

11 pages, LaTeX

References in corpus (2)

• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Solvability of the Hamiltonians related to exceptional root spaces: rational case

Cited by in corpus (4)

• Particular Integrability and (Quasi)-exact-solvability
• The quantum $H_4$ integrable system
• From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View
• Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials. III. $E_8$ case