Schubert polynomials of types A--D |
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Authors: | Rudolf Winkel |
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Institution: | Institut für Reine und Angewandte Mathematik, RWTH Aachen,?D-52056 Aachen, Germany.E-mail: winkel@iram.rwth-aachen.de, DE
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Abstract: | Schubert polynomials of type B, C, and D have been described first by S. Billey and M. Haiman BH] using a combinatorial method.
In this paper we give a unified algebraic treatment of Schubert polynomials of types A–D in the style of the Lascoux–Schützenberger
theory in type A, i.e. Schubert polynomials are generated by the application of sequences of divided difference operators
to “top polynomials”. The use of the creation operators for Q-Schur and P-Schur functions allows us to give: (1) simple and
natural forms of the “top polynomials”, (2) formulas for the easy computation with all divided differences, (3) recursive
structures, and (4) simplified derivations of basic properties.
Received: 23 July 1998 |
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Keywords: | Mathematics Subject Classification (1991):05E15 14M15 |
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