Vandermonde determinantal ideals

TL;DR

This paper proves that the ideal generated by maximal minors of a Vandermonde matrix is both radical and Cohen-Macaulay, revealing important algebraic properties of these determinantal ideals.

Contribution

It establishes the radicalness and Cohen-Macaulay property of Vandermonde determinantal ideals, linking them to Specht polynomials with specific shapes.

Findings

The ideal is radical.

The ideal is Cohen-Macaulay.

Generated by all Specht polynomials with shape (n-k,1,...,1).

Abstract

We show that the ideal generated by maximal minors (i.e., $(k+1)$-minors) of a $(k+1) \times n$ Vandermonde matrix is radical and Cohen-Macaulay. Note that this ideal is generated by all Specht polynomials with shape $(n-k,1,...,1)$.