A Q-ANALOG OF TRANSPOSITION SYMMETRY FOR INVARIANT G-FUNCTIONS Academic Article uri icon

abstract

  • We give an algebraic construction of Milne's v[G]m(n) (; ; z) functions in terms of the matrix coefficients of certain linear operators B;z. We show that the v[G]m(n) (; ; z) functions all satisfy "transposition" symmetry if and only if z = (t,..., t) Cn, unless v[G]1(n) (; ; z) is identically zero. This transposition symmetry is a "q-analog" of that for the ordinary v[G]m(n) (; ;) polynomials of Biedenharn, Gustafson, and Milne. We also define a "q-analog" of the elementary reduced Wigner coefficients for U(n) and give both a combinatorial and representation theoretic interpretation of this definition. 1986.

published proceedings

  • JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

author list (cited authors)

  • GUSTAFSON, R. A., & MILNE, S. C.

citation count

  • 5

publication date

  • February 1986