SCHUR-FUNCTIONS, GOOD IDENTITY, AND HYPERGEOMETRIC-SERIES WELL POISED IN SU(N) Academic Article uri icon

abstract

  • A simple direct proof is given of a fundamental identity involving Schur functions which contains as special cases the identity responsible for Good's proof of the Dyson conjecture and the summation theorem of Biedenharn and Louck that appears frequently in dealing with the explicit matrix elements which arise in the unitary groups. By using the Weyl character formula, a general identity is obtained which implies our result involving Schur functions when a root system of type An - 1 is considered. As a further application of our general identity, explicit analogs of Good's identity are given, corresponding to the root systems of types Bn, Cn, and Dn. In addition, methods to obtain q-analogs of all of these results are briefly described. 1983.

published proceedings

  • ADVANCES IN MATHEMATICS

author list (cited authors)

  • GUSTAFSON, R. A., & MILNE, S. C.

citation count

  • 22

complete list of authors

  • GUSTAFSON, RA||MILNE, SC

publication date

  • January 1983