Power of a determinant with two physical applications
1999 ◽
Vol 22
(4)
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pp. 745-759
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Keyword(s):
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 the 3 F2hypergeometric 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.
1993 ◽
Vol 48
(15)
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pp. 11435-11438
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2008 ◽
Vol 23
(09)
◽
pp. 1327-1336
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1994 ◽
Vol 27
(12)
◽
pp. 4211-4219
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1993 ◽
Vol 07
(14)
◽
pp. 2655-2665
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1993 ◽
Vol 08
(14)
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pp. 1297-1303
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Keyword(s):
1997 ◽
Vol 11
(06)
◽
pp. 239-244
◽
Keyword(s):
1996 ◽
Vol 10
(12)
◽
pp. 523-529
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Keyword(s):