Multivariable Vandermonde determinants, amalgams of matrices and Specht modules
Year: 2025
Type: article
Abstract: Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of a matrix which is 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.
Source: Journal of Algebra
Author: Francis Brown
Institution: University of Oxford
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,310
OpenAlex ID: W4409360259