Double Schubert polynomials and degeneracy loci for the classical groups

Details Double Schubert polynomials and degeneracy loci for the classical groups Double Schubert polynomials and degeneracy loci for the classical groups

2000-11-01

arxiv.org/abs/math/0011010v3

Annales de l'Institut Fourier 52 (2002), 1681-1727

Mathematics

Algebraic Geometry

34 pages, LaTeX; final version

Scientific paper

We propose a theory of double Schubert polynomials P_w(X,Y) for the Lie types B, C, D which naturally extends the family of Lascoux of Schutzenberger in type A. These polynomials satisfy positivity, orthogonality, and stability properties, and represent the classes of Schubert varieties and degeneracy loci of vector bundles. When w is a maximal Grassmannian element of the Weyl group, P_w(X,Y) can be expressed in terms of Schur-type determinants and Pfaffians, in analogy with the type A formula of Kempf and Laksov. An example, motivated by quantum cohomology, shows that there are no Chern class formulas for degeneracy loci of ``isotropic morphisms'' of bundles.

Affiliated with

Also associated with

No associations

Rating

Double Schubert polynomials and degeneracy loci for the classical groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Double Schubert polynomials and degeneracy loci for the classical groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Double Schubert polynomials and degeneracy loci for the classical groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-453375