arXiv math/01060792001-06math.RTmath.CO

Combinatorics and invariant differential operators on multiplicity free spaces

Friedrich Knop

备注：: 36 pages, some typos corrected
发表信息：: J. Algebra 260 (2003), 194-229
DOI：: 10.1016/S0021-8693(02)00633-6

英文摘要：

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.

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