POWERS OF THE VANDERMONDE DETERMINANT AND THE QUANTUM HALL-EFFECT

The expansion of the Laughlin ansatz for describing the ground-state w avefunction for the fractional quantum Hall effect as a linear combina tion of Slater determinantal wavefunctions for N particles is discusse d in terms of the corresponding expansion of even powers of the Vander monde alternant into Schur functions. Two new algorithms for computing the coefficients of the complete expansion are given. They appear to be substantially more efficient than other methods and avoid any use o f symmetric group characters. A number of examples are given and the r esults obtained for N = 7, 8 and 9 reviewed. The separate calculation of individual coefficients is also discussed.