Affordable Access

Double Schubert polynomials and degeneracy loci for the classical groups

Authors
Publication Date
Disciplines
  • Law

Abstract

Double Schubert polynomials and degeneracy loci for the classical groups AN N A L E S D E L’INSTI T U T F O U R IE R ANNALES DE L’INSTITUT FOURIER Andrew KRESCH & Harry TAMVAKIS Double Schubert polynomials and degeneracy loci for the classical groups Tome 52, no 6 (2002), p. 1681-1727. <http://aif.cedram.org/item?id=AIF_2002__52_6_1681_0> © Association des Annales de l’institut Fourier, 2002, tous droits réservés. L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute re- production en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement per- sonnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/ 1681- DOUBLE SCHUBERT POLYNOMIALS AND DEGENERACY LOCI FOR THE CLASSICAL GROUPS by A. KRESCH* and H. TAMVAKIS* 0. Introduction. In recent years there has been interest in finding natural polynomials that represent the classes of Schubert varieties and degeneracy loci of vector bundles (see [Tu] and [FP] for expositions). Our aim here is to define and study polynomials which we propose as type B, C and D double Schubert polynomials. Special cases of these polynomials provide orthogonal and symplectic analogues of the determinantal formula of Kempf and Laksov [KL]. For the general linear group the corresponding objects are the double Schubert polynomials Y), w E Sn ) of Lascoux and Schiitzenberger [LS] [L]. These type A polynomials possess a series of remarkable properties, and it is desirable to have a theory for the other types with as many of them as possible. Fomin and Kirillov [FK] have shown that a theory of (single) Schubert

There are no comments yet on this publication. Be the first to share your thoughts.