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1
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Symmetric polynomials and divided differences in formulas of intersection theory

100%
Pragacz P.
Banach Center Publications
|
1996
|
tom 36
|
nr 1
125-177
EN
The goal of this paper is at least two-fold. First we attempt to give a survey of some recent (and developed up to the time of the Banach Center workshop Parameter Spaces, February '94) applications of the theory of symmetric polynomials and divided differences to intersection theory. Secondly, taking this opportunity, we complement the story by either presenting some new proofs of older results (and this takes place usually in the Appendices to the present paper) or providing some new results which arose as by-products of the author's work in this domain during last years.
2
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Cycles of isotropic subspaces and formulas for symmetric degeneracy loci

75%
Pragacz P.
Banach Center Publications
|
1990
|
tom 26
|
nr 2
189-199
3
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A Pieri-type formula for even orthogonal Grassmannians

64%
Pragacz P., Ratajski J.
Fundamenta Mathematicae
|
2003
|
tom 178
|
nr 1
49-96
EN
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 of "barred permutations" with even numbers of bars, and divided differences associated with the even orthogonal group SO(2m).
4
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Positivity of Schur function expansions of Thom polynomials

64%
Pragacz P., Weber A.
Fundamenta Mathematicae
|
2007
|
tom 195
|
nr 1
85-95
EN
Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.
5
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Positivity of Thom polynomials II: the Lagrange singularities

51%
Mikosz M., Pragacz P., Weber A.
Fundamenta Mathematicae
|
2009
|
tom 202
|
nr 1
65-79
EN
We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.
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