Architectonics of Alain Lascoux's preferred formulas. (Architectonique des formules préférées d'Alain Lascoux.)
Pragacz, Piotr (2004)
Séminaire Lotharingien de Combinatoire [electronic only]
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Pragacz, Piotr (2004)
Séminaire Lotharingien de Combinatoire [electronic only]
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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.
Andrew Kresch, Harry Tamvakis (2002)
Annales de l’institut Fourier
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We propose a theory of double Schubert polynomials for the Lie types , , which naturally extends the family of Lascoux and Schützenberger in type . These polynomials satisfy positivity, orthogonality and stability properties, and represent the classes of Schubert varieties and degeneracy loci of vector bundles. When is a maximal Grassmannian element of the Weyl group, can be expressed in terms of Schur-type determinants and Pfaffians, in analogy with the type formula of...
Knutson, Allen (2001)
Experimental Mathematics
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Jean-Claude Hausmann, Allen Knutson (1998)
Annales de l'institut Fourier
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We compute the integer cohomology rings of the “polygon spaces”introduced in [F. Kirwan, Cohomology rings of moduli spaces of vector bundles over Riemann surfaces, J. Amer. Math. Soc., 5 (1992), 853-906] and [M. Kapovich & J. Millson, the symplectic geometry of polygons in Euclidean space, J. of Diff. Geometry, 44 (1996), 479-513]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we calculate its kernel using ideas from...
Molev, A.I. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Piotr Pragacz, Jan Ratajski (2003)
Fundamenta Mathematicae
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We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions...
McNamara, Peter J. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Hironobu Kimura (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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