Power of a determinant with two physical applications
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.
scientific article; zbMATH DE number 1417973