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International Journal of Mathematics and Mathematical Sciences - Volume 22 1999, Issue 4, Pages 745-759

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

Received 29 September 1997; Revised 7 May 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An expression for the kth power of an n×n determinant in n2 indeterminates 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 group SU2, noting also the relation to the  3 F2 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.





Author: James D. Louck

Source: https://www.hindawi.com/



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