Pieri's Formula for Generalized Schur Polynomials

Details Pieri's Formula for Generalized Schur Polynomials Pieri's Formula for Generalized Schur Polynomials

2006-06-16

arxiv.org/abs/math/0606386v2

J. Algebraic Combin. 26 (2007), no. 1, 27-45

Mathematics

Combinatorics

Scientific paper

10.1007/s10801-006-0047-y

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.

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