Article ID Journal Published Year Pages File Type
4587523 Journal of Algebra 2008 21 Pages PDF
Abstract

We derive a Jacobi–Trudi type formula for Jack functions of rectangular shapes. In this formula, we make use of a hyperdeterminant, which is Cayley's simple generalization of the determinant. In addition, after developing the general theory of hyperdeterminants, we give summation formulas for Schur functions involving hyperdeterminants, and evaluate Toeplitz type hyperdeterminants by using Jack function theory.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory