Fonctions symétriques, polynomes de Schubert et lieux de dégénérescence / Laurent Manivel

Auteur principal : Manivel, Laurent, 1965-, AuteurType de document : MonographieCollection : Cours spécialisés, 3Langue : français.Pays: France.Éditeur : Paris : Société Mathématique de France, 1998Description : 1 vol. (VI-179 p.) : fig. ; 24 cmISBN: 9782856290668.ISSN: 1284-6090.Bibliographie : Bibliogr. p. [171]-176. Index.Sujet MSC : 14M15, Algebraic geometry - Special varieties, Grassmannians, Schubert varieties, flag manifolds
05E10, Algebraic combinatorics, Combinatorial aspects of representation theory
05E05, Algebraic combinatorics, Symmetric functions and generalizations
14N10, Projective and enumerative algebraic geometry, Enumerative problems (combinatorial problems)
20C30, Group theory - Representation theory of groups, Representations of finite symmetric groups
En-ligne : Résumé
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 Monographie Monographie CMI
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Bibliogr. p. [171]-176. Index

This text grew out of an advanced course that the author taught at the Fourier Institute (Grenoble, France) during the 1995-96 academic year. The first part (chapter I) is of purely algebraic-combinatorial nature and provides a modern, very thorough introduction to the classical topic of symmetric functions, with a special emphasis on the combinatorics of Schur polynomials. ... The second part (chapter II) is devoted to the study of the so-called Schubert polynomials, which were introduced by A. Lascoux and M.-P. Schützenberger about twenty years ago. These polynomials, defined in terms of divided differences, are closely related to the Bruhat order on symmetric groups as well as to certain Hecke algebras of these groups, to the celebrated Yang-Baxter equation, and to certain Schur functions. (Zentralblatt)

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