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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.

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