Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials

Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type models. As applications, raising operators and shift operators for such polynomials are constructed.Comment: 26 pages, LaTeX using epsf.sty, one figur

Solutions to the KP hierarchy with an elliptic background

A class of "elliptic soliton" solutions of the Kadomtsev-Petviashvili hierarchy, which includes a determinantal solution of Li and Zhang, is described in terms of pseudo-differential operator formulation. In our approach, the Li-Zhang solution is obtained by repeatedly applying the Darboux transformation to a stationary solution. Real-valued solutions are discussed and various examples that display web-like patterns are presented.Comment: 31 pages, 6 figure

Yang-Baxter Maps from the Discrete BKP Equation

We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP equation

Dressing method and the coupled KP hierarchy

The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the 2-component KP hierarchy.Comment: 11 pages, LaTeX, no figure