Hankel hyperdeterminants, rectangular Jack polynomials and even powers of the Vandermonde

TL;DR

This paper explores the relationship between rectangular Jack polynomials and Hankel hyperdeterminants, providing a new expression for even powers of the Vandermonde in terms of Jack polynomials.

Contribution

It establishes a novel connection between Jack polynomials and hyperdeterminants, and expresses even powers of the Vandermonde using Jack polynomials.

Findings

Derived an explicit expression for even powers of the Vandermonde in terms of Jack polynomials.

Linked Hankel hyperdeterminants with rectangular Jack polynomials.

Enhanced understanding of algebraic structures involving Jack polynomials.

Abstract

We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials.