Combinatorics and invariant differential operators on multiplicity free spaces
Representation Theory
2013-10-25 v2 Combinatorics
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.
Cite
@article{arxiv.math/0106079,
title = {Combinatorics and invariant differential operators on multiplicity free spaces},
author = {Friedrich Knop},
journal= {arXiv preprint arXiv:math/0106079},
year = {2013}
}
Comments
36 pages, some typos corrected