Power of a determinant with two physical applications
type: Item
instance of: scholarly article
title: Power of a determinant with two physical applications
zbMATH Open document ID: 0953.15010
DOI: 10.1155/S0161171299227457
author: J. D. Louck
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2001-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/48603
review text: Using a combinatorial expression for the \(k\)th power of a determinant of a square matrice, the author considers two applications. The first one is the Regge generating function for the Clebsch-Gordan coefficients of the unitary group \(SU(2)\), which are also related to the \(_{3}F_{2}\) hypergeometric series. The second is the even power of the Vandermonde determinant, which leads to an interesting map between magic square arrays and partitions, with applications to the wave functions describing the quantum Hall effect.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 15A90
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1417973
zbMATH Keywords: power of a determinant
zbMATH Keywords: Clebsch-Gordan coefficients
zbMATH Keywords: Vandermonde determinant
zbMATH Keywords: magic squares
zbMATH Keywords: unitary group
zbMATH Keywords: hypergeometric series
zbMATH Keywords: wave functions
zbMATH Keywords: quantum Hall effect
describes a project that uses: SCHUR
MaRDI profile type: Publication
OpenAlex ID: W2038177730
description: scientific article; zbMATH DE number 1417973