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Degeneration of Schubert varieties of S L n / B to toric varieties

Raika Dehy, Rupert W.T. Yu (2001)

Annales de l’institut Fourier

Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of S L n to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule G / P to Schubert varieties in S L n .

Double Schubert polynomials and degeneracy loci for the classical groups

Andrew Kresch, Harry Tamvakis (2002)

Annales de l’institut Fourier

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 and Schützenberger 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....

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