Binomial coefficients and Littlewood-Richardson coefficients for Jack polynomials

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Abstract

In this paper, we consider translation and multiplication operators acting on the rings of symmetric and nonsymmetric polynomials and study their matrix coefficients with respect to the bases of Jack polynomials and interpolation polynomials. The main new insight is that the symmetric and nonsymmetric cases share a key combinatorial feature, that of a locally finite graded poset with a minimum element. This allows us to treat both cases in a simple and unified manner.

Original languageEnglish (US)
Pages (from-to)1597-1612
Number of pages16
JournalInternational Mathematics Research Notices
Volume2011
Issue number7
DOIs
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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