Combinatorics and invariant differential operators on multiplicity free spaces
arXiv:math/0106079 · doi:10.1016/S0021-8693(02)00633-6
Abstract
We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result now is the "transposition formula", a generalization of Okounkov's binomial theorem (q-alg/9608021) for shifted Jack polynomials. From this formula, we derive an interpolation formula, an evaluation formula, a scalar product, a binomial theorem, and properties of the algebra generated by the multiplication and difference operators.
36 pages, some typos corrected
References in corpus (5)
- Shifted Schur Functions
- Difference equations and symmetric polynomials defined by their zeros
- Shifted Jack polynomials, binomial formula, and applications
- Semisymmetric polynomials and the invariant theory of matrix vector pairs
- Construction of commuting difference operators for multiplicity free spaces