Tableaux statistics for two part Macdonald polynomials
Abstract
The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the $q,t$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 $q,t$Kostka coefficients by assigning a statistic in $q$ and $t$ to each standard tableau.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9812001
 arXiv:
 arXiv:math/9812001
 Bibcode:
 1998math.....12001L
 Keywords:

 Combinatorics;
 Quantum Algebra;
 05Exx
 EPrint:
 19 pages