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Showing 1 to 10 of 10 for “"Schubert calculus"”.
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Equivariant Schubert calculus and applications
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Schubert calculus in generalized cohomology
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
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Cotangent Schubert Calculus in Grassmannians
… formulas for the Segre-MacPherson classes of Schubert cells in T-equivariant cohomology and the motivic Segre classes of Schubert cells in T-equivariant K-theory. In doing so we look at the pushforward of the projection map from the Bott-Samelson (Kempf-Laksov) desingularization to the …
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K-theoretic Schubert calculus and applications
… of Grassmannians. A major theme of the modern Schubert calculus is to extend this rule and its associated combinatorics to richer cohomology theories. This thesis focuses on K-theoretic Schubert calculus. We prove the first Littlewood-Richardson rule in torus-equivariant K-theory. We thereby …
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Root-theoretic Young diagrams and Schubert Calculus
… to find nonnegative combinatorial rules for the Schubert calculus of generalized flag varieties; that is, for the structure constants of their cohomology rings with respect to the Schubert basis. There are several natural choices of combinatorial indexing sets for the Schubert basis classes. This …
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Matrix Schubert varieties for the affine Grassmannian
Schubert calculus has become an indispensable tool for enumerative geometry. It concerns the multiplication of Schubert classes in the cohomology of flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The …
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Symmetric structures in the weak and strong Bruhat orders
… rich combinatorial objects, with connections to Schubert calculus, Lie algebras, hyperplane arrangements, sorting networks and so on. In this thesis, we study various new symmetries within these structures, including the balance constant and the hull metric property of the weak order, and the …
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Root polytopes, triangulations, and subdivision algebras
… the main outstanding problem of modern Schubert calculus, that of finding a combinatorial interpretation for the structure constants of Schubert polynomials. Using a geometric understanding of the relations of Kirillov's algebras in terms of subdivisions of root polytopes, several …
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Polynomials in algebraic combinatorics
… and connect it to the Newton polytopes of the Schubert polynomials and the key polynomials. Semistandard skyline fillings are a combinatorial model that arises from specializing the combinatorics of Macdonald polynomials. We define a set-valued extension which allows us to define inhomogeneous …
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Dual Filtered Graphs for Kac-Moody algebras
We construct a strong filtered graph $\Gamma_s(\Lambda)$ dependent on the dominant weight $\Lambda$, and a weak filtered graph $\Gamma_w(\Kcen)$ dependent on the canonical central element $\Kcen$ for an arbitrary Kac-Moody algebra $g$. In our construction, both graphs $(\Gamma_s(\Lambda), …