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Pieri's Formula for Generalized Schur Polynomials

Yasuhide Numata
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Abstract

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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Yasuhide Numata. 2006-06-16. Pieri's Formula for Generalized Schur Polynomials. https://doi.org/10.1007/s10801-006-0047-y

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