Combinatorics and invariant theory of multiplicity free spaces
We study the generalization of shifted Jack polynomials to arbitrary
multiplicity free spaces. In a previous
paper 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 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.
Appeared in: J. Algebra 260 (2003) 194-229
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Last updated: March 20, 2003