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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....

Elliptic curves on spinor varieties

Nicolas Perrin (2012)

Open Mathematics

We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.

Equivariant K-theory of flag varieties revisited and related results

V. Uma (2013)

Colloquium Mathematicae

We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring K T ( G / B ) of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in K T ( G / B ) to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of K ( X ) where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of...

Exceptional collections on isotropic Grassmannians

Alexander Kuznetsov, Alexander Polishchuk (2016)

Journal of the European Mathematical Society

We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.

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