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Title: Power of a determinant with two physical applications

Abstract

An expression for the k th power of an n × n determinant in n 2 indeterminates ( z i j ) is given as a sum of monomials. Two applications of this expression are given: the first is the Regge generating function for the Clebsch-Gordan coefficients of the unitary group S U ( 2 ) , noting also the relation to the 3 F 2 hypergeometric series; the second is to the even powers of the Vandermonde determinant, or, equivalently, all powers of the discriminant. The second result leads to an interesting map between magic square arrays and partitions and has applications to the wave functions describing the quantum Hall effect. The generalization of this map to arbitrary square arrays of nonnegative integers, having given row and column sums, is also given.

Authors:
 [1]
  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1198451
Grant/Contract Number:  
W-7405-ENG-36
Resource Type:
Published Article
Journal Name:
International Journal of Mathematics and Mathematical Sciences
Additional Journal Information:
Journal Name: International Journal of Mathematics and Mathematical Sciences Journal Volume: 22 Journal Issue: 4; Journal ID: ISSN 0161-1712
Publisher:
Hindawi Publishing Corporation
Country of Publication:
Country unknown/Code not available
Language:
English

Citation Formats

Louck, James D. Power of a determinant with two physical applications. Country unknown/Code not available: N. p., 1999. Web. doi:10.1155/S0161171299227457.
Louck, James D. Power of a determinant with two physical applications. Country unknown/Code not available. doi:10.1155/S0161171299227457.
Louck, James D. Fri . "Power of a determinant with two physical applications". Country unknown/Code not available. doi:10.1155/S0161171299227457.
@article{osti_1198451,
title = {Power of a determinant with two physical applications},
author = {Louck, James D.},
abstractNote = {An expression for the k th power of an n × n determinant in n 2 indeterminates ( z i j ) is given as a sum of monomials. Two applications of this expression are given: the first is the Regge generating function for the Clebsch-Gordan coefficients of the unitary group S U ( 2 ) , noting also the relation to the   3   F 2 hypergeometric series; the second is to the even powers of the Vandermonde determinant, or, equivalently, all powers of the discriminant. The second result leads to an interesting map between magic square arrays and partitions and has applications to the wave functions describing the quantum Hall effect. The generalization of this map to arbitrary square arrays of nonnegative integers, having given row and column sums, is also given.},
doi = {10.1155/S0161171299227457},
journal = {International Journal of Mathematics and Mathematical Sciences},
number = 4,
volume = 22,
place = {Country unknown/Code not available},
year = {1999},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1155/S0161171299227457

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