  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.
