Affine insertion and Pieri rules for the affine Grassmannian / Thomas Lam, Luc Lapointe, Jennifer Morse,... [et al.]

Auteur: Lam, Thomas (1980-) - AuteurCo-auteur: Lapointe, Luc (1970-) - Auteur ; Morse, Jennifer (1971-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 977Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 2010Description: 1 vol. (XI-82 p.) : fig. ; 26 cm ISBN: 9780821846582 ; br. Résumé: The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C).Their main results are: - Pieri rules for the Schubert bases of H*(Gr) and H∗(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. - A new combinatorial definition for k-Schur functions, which represent the Schubert basis of H∗(Gr). - A combinatorial interpretation of the pairing H*(Gr)×H∗(Gr)→Z induced by the cap product. (Source : AMS).Bibliographie: Bibliogr. p. 81-82. Sujets MSC: 14-02 Algebraic geometry -- Research exposition (monographs, survey articles)
14N15 Algebraic geometry -- Projective and enumerative geometry -- Classical problems, Schubert calculus
05E15 Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of groups and algebras
En-ligne: Arxiv | Site de l'auteur
Location Call Number Status Date Due
Salle R 08601-01 / Séries AMS (Browse Shelf) Available

Bibliogr. p. 81-82

The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C).Their main results are:
- Pieri rules for the Schubert bases of H*(Gr) and H∗(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes.
- A new combinatorial definition for k-Schur functions, which represent the Schubert basis of H∗(Gr).
- A combinatorial interpretation of the pairing H*(Gr)×H∗(Gr)→Z induced by the cap product. (Source : AMS)

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