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Schubert polynomials. (English) Zbl 0784.05061
Surveys in combinatorics, Proc. 13th Br. Comb. Conf., Guildford/UK 1991, Lond. Math. Soc. Lect. Note Ser. 166, 73-99 (1991).
[For the entire collection see Zbl 0728.00006.]
This article gives an informative survey of the combinatorial theory of Schubert polynomials developed by A. Lascoux and M.-P. Sch├╝tzenberger. Its topic may be described by the titles of the sections and subsections: Permutations (Bruhat order, diagrams and codes, vexillary permutations); divided differences; multi-Schur functions (duality); Schubert polynomials; orthogonality; double Schubert polynomials. In many cases proofs have been omitted.

MSC:
05E05 Symmetric functions and generalizations
05E15 Combinatorial aspects of groups and algebras (MSC2010)
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
14M15 Grassmannians, Schubert varieties, flag manifolds