%0 Journal Article
%T Pieri's Formula for Generalized Schur Polynomials
%A Yasuhide Numata
%J Mathematics
%D 2006
%I arXiv
%R 10.1007/s10801-006-0047-y
%X 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.
%U http://arxiv.org/abs/math/0606386v2