Displaying similar documents to “Architectonics of Alain Lascoux's preferred formulas. (Architectonique des formules préférées d'Alain Lascoux.)”

Pieri's formula for flag manifolds and Schubert polynomials

Frank Sottile (1996)

Annales de l'institut Fourier

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We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary or a complete symmetric polynomial. Thus, we generalize the classical Pieri’s formula for Schur polynomials (associated to Grassmann varieties) to Schubert polynomials (associated to flag manifolds). Our primary technique is an explicit geometric description...

Double Schubert polynomials and degeneracy loci for the classical groups

Andrew Kresch, Harry Tamvakis (2002)

Annales de l’institut Fourier

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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...

Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces

László Fehér, Richárd Rimányi (2003)

Open Mathematics

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The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.