The Prism tableau model for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1; x2; : : :]. We suggest the prism tableau model for these polynomials.
Anna Weigandt, Alexander Yong
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Order recognition by Schubert polynomials generated by optical near-field statistics via nanometre-scale photochromism [PDF]
Scientific Reports, 2022 Irregular spatial distribution of photon transmission through a photochromic crystal photoisomerized by a local optical near-field excitation was previously reported, which manifested complex branching processes via the interplay of material deformation ...
Kazuharu Uchiyama +8 more
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Double Schubert polynomials for the classical Lie groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 For each infinite series of the classical Lie groups of type $B$, $C$ or $D$, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank.
Takeshi Ikeda +2 more
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Schur and Schubert polynomials as Thom polynomials—cohomology of moduli spaces
Central European Journal of Mathematics, 2003 Richárd Rimányi, László Gy. Fehér
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Combinatorial description of the cohomology of the affine flag variety [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigatethe combinatorics of affine Schubert calculus for typeA. We introduce Murnaghan-Nakayama elements and Dunklelements in the affine FK algebra.
Seung Jin Lee
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A dual approach to structure constants for K-theory of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants
Huilan Li, Jennifer Morse, Pat Shields
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Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 In their 1987 paper Kraskiewicz and Pragacz defined certain modules, which we call KP modules, over the upper triangular Lie algebra whose characters are Schubert polynomials.
Masaki Watanabe
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Double Schubert polynomials do have saturated Newton polytopes
Forum of Mathematics, Sigma, 2023 We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees.
Federico Castillo +3 more
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Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a ...
Masaki Watanabe
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On Schubert calculus in elliptic cohomology [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points.
Cristian Lenart, Kirill Zainoulline
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