Title: Vector-valued Jack Polynomials and Wavefunctions on the Torus,
Abstract: The Hamiltonian of the quantum Calogero-Sutherland model of $N$ identical
particles on the circle with $1/r^{2}$ interactions has eigenfunctions
consisting of Jack polynomials times the base state. By use of the generalized
Jack polynomials taking values in modules of the symmetric group and the matrix
solution of a system of linear differential equations one constructs novel
eigenfunctions of the Hamiltonian. Like the usual wavefunctions each
eigenfunction determines a symmetric probability density on the $N$-torus. The
construction applies to any irreducible representation of the symmetric group.
The methods depend on the theory of generalized Jack polynomials due to
Griffeth, and the Yang-Baxter graph approach of Luque and the author.