Pieri’s formula for generalized Schur polynomials |
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Authors: | Yasuhide Numata |
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Institution: | (1) Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo Hokkaido, 060-0810, Japan |
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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 commutation relation of generalized Schur operators implies Pieri's formula for generalized
Schur polynomials. |
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Keywords: | Pieri formula Generarized Schur operators Schur polynomials Young diagrams Planar binary trees Differential posets Dual graphs Symmetric functions Quasi-symmetric polynomials |
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