Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-30
Annals Phys. 316 (2005) 187-212
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, no figures; Refs. added, version to appear in Annals of Physics
Scientific paper
10.1016/j.aop.2004.11.007
We make a generalization of the type C monomial space of a single variable, which was introduced in the construction of type C N-fold supersymmetry, to several variables. Then, we construct the most general quasi-solvable second-order operators preserving this multivariate type C space. These operators of several variables are characterized by the fact that two different polynomial type solutions are available. In particular, we investigate and classify all the possible Schroedinger operators realized as a subclass of this family. It turns out that the rational, hyperbolic, and trigonometric Calogero-Sutherland models as well as some particular type of the elliptic Inozemtsev system, all associated with the BC_M root system, fall within the class.
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