Results 11 to 20 of about 12,632 (221)
Back stable Schubert calculus [PDF]
Compositio Mathematica, 2021 We study the back stable Schubert calculus of the infinite flag variety. Our main results are:–a formula for back stable (double) Schubert classes expressing them in terms of a symmetric function part and a finite part;–a novel definition of double and triple Stanley symmetric functions;–a proof of the positivity of double Edelman–Greene coefficients ...
Lam, Thomas +2 more
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An equivariant rim hook rule for quantum cohomology of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis.
Elizabeth Beazley +2 more
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Root-theoretic Young Diagrams, Schubert Calculus and Adjoint Varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Root-theoretic Young diagrams are a conceptual framework to discuss existence of a root-system uniform and manifestly non-negative combinatorial rule for Schubert calculus.
Dominic Searles, Alexander Yong
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Flag Gromov-Witten invariants via crystals [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of ...
Jennifer Morse, Anne Schilling
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Multiplicity-Free Schubert Calculus [PDF]
Canadian Mathematical Bulletin, 2010 AbstractMultiplicity-free algebraic geometry is the study of subvarieties Y ⊆ X with the “smallest invariants” as witnessed by a multiplicity-free Chow ring decomposition of [Y] ∈ A*(X) into a predetermined linear basis.This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis.
Thomas, Hugh, Yong, Alexander
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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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Generalized Permutahedra and Schubert Calculus
Arnold Mathematical Journal, 2022 We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety. Our argument utilizes recent developments in the study of Schubitopes, which are Newton polytopes of Schubert polynomials. The resulting tableau test executes in polynomial time.
Avery St. Dizier, Alexander Yong
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Equivariant Giambelli formula for the symplectic Grassmannians — Pfaffian Sum Formula [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We prove an explicit closed formula, written as a sum of Pfaffians, which describes each equivariant Schubert class for the Grassmannian of isotropic subspaces in a symplectic vector ...
Takeshi Ikeda, Tomoo Matsumura
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An inequality of Kostka numbers and Galois groups of Schubert problems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka ...
Christopher J. Brooks +2 more
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Cohomology classes of rank varieties and a counterexample to a conjecture of Liu [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 To each finite subset of a discrete grid $\mathbb{N}×\mathbb{N}$ (a diagram), one can associate a subvariety of a complex Grassmannian (a diagram variety), and a representation of a symmetric group (a Specht module).
Brendan Pawlowski
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