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Combinatorics and invariant theory of multiplicity free spaces | Friedrich Knop
; | Date: |
11 Jun 2001 | Journal: | J. Algebra 260 (2003), 194-229 | Subject: | Representation Theory; Combinatorics MSC-class: 05E35;33C52;39A70 | math.RT math.CO | 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. | Source: | arXiv, math.RT/0106079 | Services: | Forum | Review | PDF | Favorites |
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