English

Tableaux statistics for two part Macdonald polynomials

Combinatorics 2007-05-23 v1 Quantum Algebra

Abstract

The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the q,tq,t-Kostka polynomials. We define operators to build standard tableaux and show that they are equivalent to creation operators that recursively build the Macdonald polynomials indexed by two part partitions. We uncover a new basis for these particular Macdonald polynomials and in doing so are able to give an explicit description of their associated q,tq,t-Kostka coefficients by assigning a statistic in qq and tt to each standard tableau.

Keywords

Cite

@article{arxiv.math/9812001,
  title  = {Tableaux statistics for two part Macdonald polynomials},
  author = {L. Lapointe and J. Morse},
  journal= {arXiv preprint arXiv:math/9812001},
  year   = {2007}
}

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19 pages