Pieri's Formula for Generalized Schur Polynomials
Combinatorics
2011-04-19 v2
Abstract
Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutating relation of generalized Schur operators implies Pieri's formula to generalized Schur polynomials.
Cite
@article{arxiv.math/0606386,
title = {Pieri's Formula for Generalized Schur Polynomials},
author = {Yasuhide Numata},
journal= {arXiv preprint arXiv:math/0606386},
year = {2011}
}