English

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.

Keywords

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

R2 v1 2026-07-22T16:39:05.081Z