PIERI’S FORMULA FOR GENERALIZED SCHUR POLYNOMIALS

Abstract. Young’s lattice is a prototypical example of differential posets. Differential posets have the Robinson correspondence, the correspondence between permutations and pairs of standard tableaux with the same shape, as in the case of Young’s lattice. Fomin introduced generalized Schur operators to generalize the method of Robinson correspondence in differential posets to the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard tableaux with the same shape. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We generalize the Pieri’s formula to the generalized Schur polynomials. 1.