Power of a determinant with two physical applications

Author:

Louck James D.1

Affiliation:

1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Abstract

An expression for thekth power of ann×ndeterminant inn2indeterminates(zij)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 groupSU(2), noting also the relation to the3F2hypergeometric 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.

Funder

U.S. Department of Energy

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Angular Momentum Theory;Springer Handbook of Atomic, Molecular, and Optical Physics;2023

2. Angular Momentum Theory;Springer Handbook of Atomic, Molecular, and Optical Physics;2006

3. Angular momentum theory, umbral calculus, and combinatorics;Computers & Mathematics with Applications;2001-05

4. The Future of Quantum Theory of Angular Momentum;Essays on the Future;2000

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