Multivariable Vandermonde determinants, amalgams of matrices and Specht modules
Representation Theory
2026-04-23 v1 Combinatorics
Group Theory
Abstract
Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of matrices which are obtained by amalgamating the entries of two smaller matrices. In particular, this gives formulae for multivariable Vandermonde determinants as a sum of completely factorising terms, each of which is a Vandermonde determinant in fewer variables. As an application, we deduce an elementary proof of the multiplicativity of the transfinite diameter for products of compact sets.
Keywords
Cite
@article{arxiv.2604.20390,
title = {Multivariable Vandermonde determinants, amalgams of matrices and Specht modules},
author = {Francis Brown},
journal= {arXiv preprint arXiv:2604.20390},
year = {2026}
}