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Related papers: Quantum K theory of symplectic Grassmannians

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We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation…

Algebraic Geometry · Mathematics 2025-09-05 Wei Gu , Leonardo C. Mihalcea , Eric Sharpe , Hao Zou

We prove that the Schubert structure constants of the quantum K-theory rings of symplectic Grassmannians of lines have signs that alternate with codimension and vanish for degrees at least 3. We also give closed formulas that characterize…

Algebraic Geometry · Mathematics 2024-02-20 Vladimiro Benedetti , Nicolas Perrin , Weihong Xu

We utilize physics arguments, and the nonabelian/abelian correspondence, to relate the Givental and Lee's quantum K theory ring of Grassmannians to a twisted variant of the quantum cohomology ring. Furthermore, the quantum K pairing is…

High Energy Physics - Theory · Physics 2024-07-17 Wei Gu , Jirui Guo , Leonardo Mihalcea , Yaoxiong Wen , Xiaohan Yan

We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N).…

High Energy Physics - Theory · Physics 2020-10-28 Hans Jockers , Peter Mayr , Urmi Ninad , Alexander Tabler

In this paper we use three-dimensional gauged linear sigma models to make physical predictions for Whitney-type presentations of equivariant quantum K theory rings of partial flag manifolds, as quantum products of universal subbundles and…

High Energy Physics - Theory · Physics 2024-02-08 W. Gu , L. Mihalcea , E. Sharpe , W. Xu , H. Zhang , H. Zou

We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate K-theory of Grassmannians to a bialgebra…

Algebraic Geometry · Mathematics 2007-05-23 Anders Skovsted Buch

This work is devoted to the study of the foundations of quantum K-theory, a K-theoretic version of quantum cohomology theory. In particular, it gives a deformation of the ordinary K-ring K(X) of a smooth projective variety X, analogous to…

Algebraic Geometry · Mathematics 2022-01-12 Y. -P. Lee

Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the classical flag variety Fl_n, we define and study quantum Grothendieck…

Combinatorics · Mathematics 2007-05-23 C. Lenart , T. Maeno

Odd symplectic Grassmannians are a generalization of symplectic Grassmannians to odd-dimensional spaces. Here we compute the classical and quantum cohomology of the odd symplectic Grassmannian of lines. Although these varieties are non…

Algebraic Geometry · Mathematics 2012-01-05 Clélia Pech

We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…

High Energy Physics - Theory · Physics 2017-08-23 Djordje Minic , Chia-Hsiung Tze

We compute the additive structure of the Hermitian $K$-theory spectrum of an even-dimensional Grassmannian over a base field $k$ of characteristic zero in terms of the Hermitian $K$-theory of $X$, using certain symmetries on Young diagrams.…

K-Theory and Homology · Mathematics 2023-09-27 Herman Rohrbach

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…

High Energy Physics - Theory · Physics 2011-10-26 Daniele Oriti

We study the quantum K-theory ring $QK(X)$ of a Grassmannian $X$ and prove a manifestly positive formula for the product of an arbitrary class by a hook class. This generalizes the quantum K-theoretic Pieri rule, a prior result of Buch and…

Combinatorics · Mathematics 2026-01-14 Joy Hamlin

We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an…

Algebraic Geometry · Mathematics 2019-12-19 Anders S. Buch , Leonardo C. Mihalcea

The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…

Quantum Physics · Physics 2012-07-10 Inge S. Helland

This is a companion to a recent investigation of K-theoretical invariants for symmetric spaces. We introduce a new class of cycles in K-groups, which are connected to elements of an underlying root lattice. This will be needed for a…

K-Theory and Homology · Mathematics 2012-10-03 Dennis Bohle , Wend Werner

This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…

Algebraic Geometry · Mathematics 2018-07-16 Paul Zinn-Justin

Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class…

Algebraic Geometry · Mathematics 2008-12-05 Anders S. Buch , Andrew Kresch , Harry Tamvakis

Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…

Mathematical Physics · Physics 2021-06-16 John Mashford

We give formulas for the products of classes of Schubert varieties in the quantum cohomology rings of Grassmannians, in terms of the combinatorics of partitions and tableaux.

alg-geom · Mathematics 2008-02-03 Aaron Bertram , Ionut Ciocan-Fontanine , William Fulton
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