Results 31 to 40 of about 12,587 (151)
Maximal Newton polygons via the quantum Bruhat graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 This paper discusses a surprising relationship between the quantum cohomology of the variety of complete flags and the partially ordered set of Newton polygons associated to an element in the affine Weyl group.
Elizabeth T. Beazley
doaj +1 more source
Eigenvalue Inequalities and Schubert Calculus [PDF]
Mathematische Nachrichten, 1995 AbstractUsing techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A1,…, Ar ϵ ¢n×n with the spectrum of the sum A1 + … + Ar. These extend eigenvalue inequalities due to Freede‐Thompson and Horn for sums of eigenvalues of two Hermitian matrices.
Helmke, U, Rosenthal, J
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Descent-Cycling in Schubert Calculus [PDF]
Experimental Mathematics, 2001 We prove two lemmata about Schubert calculus on generalized flag manifolds G/B, and in the case of the ordinary flag manifold GL_n/B we interpret them combinatorially in terms of descents, and geometrically in terms of missing subspaces. One of them gives a symmetry of Schubert calculus that we christen_descent-cycling_.
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Equivariant Quantum Schubert Polynomials [PDF]
, 2014 We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials.
Anderson, D., Chen, Linda
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Experimentation in the Schubert Calculus [PDF]
Advanced Studies in Pure Mathematics, 2018 Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the real Schubert calculus has been inspired by this continuing experimentation.
del Campo, Abraham Martín +1 more
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Schubert Polynomials for the affine Grassmannian of the symplectic group [PDF]
, 2009 We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions.
A. Pressley +17 more
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On the Coproduct in Affine Schubert Calculus
, 2022 25 ...
Lam, Thomas +2 more
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Gelfand-Zetlin polytopes and flag varieties [PDF]
, 2009 I construct a correspondence between the Schubert cycles on the variety of complete flags in C^n and some faces of the Gelfand-Zetlin polytope associated with the irreducible representation of SL_n(C) with a strictly dominant highest weight.
Kiritchenko, Valentina
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Positivity in equivariant Schubert calculus [PDF]
Duke Mathematical Journal, 2001 We prove a conjecture of Dale Peterson on positivity in the multiplication in the T-equivariant cohomology of the flag variety. The theorem follows from a more general positivity result about the equivariant cohomology of varieties with actions of a solvable group with finitely many orbits.
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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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