Hyperdeterminantal expressions for Jack functions of rectangular shapes
Combinatorics
2008-06-03 v4
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 formulae for Schur functions involving hyperdeterminants, and evaluate Toeplitz-type hyperdeterminants by using Jack function theory.
Cite
@article{arxiv.math/0603033,
title = {Hyperdeterminantal expressions for Jack functions of rectangular shapes},
author = {Sho Matsumoto},
journal= {arXiv preprint arXiv:math/0603033},
year = {2008}
}
Comments
18 pages. The title of 3rd version is ''Hyperdeterminant expressions ...''. The title of 1st and 2nd versions was ``Summation formulas for Schur functions involving hyperdeterminants''