Quantum trigonometric Calogero-Sutherland model and irreducible characters for the exceptional algebra E8
نویسنده
چکیده
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model for the Lie algebra E8 and coupling constant κ = 1 by using the fundamental irreducible characters of the algebra as dynamical independent variables. Then, we compute the second order characters of the algebra and some higher order characters.
منابع مشابه
Some new solutions to the Schrödinger equation for the trigonometric E8 Calogero-Sutherland problem
We provide a list of explicit eigenfunctions of the trigonometric Calogero-Sutherland Hamiltonian associated to the root system of the exceptional Lie algebra E8. The quantum numbers of these solutions correspond to the first and second order weights of the Lie algebra.
متن کاملCommon Algebraic Structure for the Calogero-Sutherland Models
We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provide an orthogonal basis for the rational case. One dimensional quantum integrable models with long-range interaction have attracted much interest, because of not...
متن کاملFrom Quantum AN (Sutherland) to E8 Trigonometric Model: Space-of-Orbits View
A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits). These models are completely-integrable and admit extra particular integrals. All of them are characterized by (i) a number of polynomial eigenfunctions and quadratic in quantum numbers eigenvalues for exactly-solvable case...
متن کاملar X iv : h ep - t h / 96 01 17 0 v 1 3 1 Ja n 19 96 Semi - infinite wedges and the conformal limit of the fermionic Calogero - Sutherland Model with spin
The conformal limit over an anti-ferromagnetic vacuum of the fermionic spin 1 2 Calogero-Sutherland Model is derived by using the wedge product formalism. The space of states in the conformal limit is identified with the Fock space of two complex fermions, or, equivalently, with a tensor product of an irreducible level-1 module of ŝl2 and a Fock space module of the Heisenberg algebra. The Hamil...
متن کاملHidden Algebras of the (super) Calogero and Sutherland models
We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the AN , BCN , BN , CN and DN Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed — for arbitrary valu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008