Pieri's Formula for Generalized Schur Polynomials
Abstract
Young's lattice, the lattice of all Young diagrams, has the RobinsonSchenstedKnuth correspondence, the correspondence between certain matrices and pairs of semistandard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the RobinsonSchenstedKnuth correspondence. In this sense, generalized Schur operators are generalizations of semistandard 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606386
 Bibcode:
 2006math......6386N
 Keywords:

 Mathematics  Combinatorics;
 05E05;
 05E99;
 05C05
 EPrint:
 J. Algebraic Combin. 26 (2007), no. 1, 2745