# 3d mirror symmetry of the cotangent bundle of the full flag variety

@article{Dinkins20203dMS,
title={3d mirror symmetry of the cotangent bundle of the full flag variety},
author={Hunter Dinkins},
journal={Letters in Mathematical Physics},
year={2020},
volume={112}
}
• Hunter Dinkins
• Published 17 November 2020
• Materials Science
• Letters in Mathematical Physics
Aganagic and Okounkov proved that the elliptic stable envelope provides the pole cancellation matrix for the enumerative invariants of quiver varieties known as vertex functions. This transforms a basis of a system of q-difference equations holomorphic in variables z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document…
8 Citations
• Mathematics
Selecta Mathematica
• 2022
In this paper we prove a formula relating the equivariant Euler characteristic of K-theoretic stable envelopes to an object known as the index vertex for the cotangent bundle of the full flag
Hunter Dinkins: One of the fundamental objects in the K -theoretic enumerative geometry of Nakajima quiver varieties is known as the the capping operator. It is uniquely determined as the fundamental
• Hunter Dinkins
• Mathematics
International Mathematics Research Notices
• 2022
We generalize Smirnov’s formula for the elliptic stable envelopes of the Hilbert scheme of points in $\mathbb {C}^2$ to the case of affine type $A$ Nakajima quiver varieties constructed with
• Mathematics
Inventiones mathematicae
• 2022
For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the
We introduce a variation of the K-theoretic quantized Coulomb branch constructed by Braverman–Finkelberg–Nakajima, by application of a new virtual intersection theory. In the abelian case, we define
We introduce a variant of the $K$-theoretic quantized Coulomb branch constructed by Braverman--Finkelberg--Nakajima, by application of a new virtual intersection theory. In the abelian case, we
• Mathematics
• 2021
We consider a pair of quiver varieties $(X;X^{\prime})$ related by 3D mirror symmetry, where $X =T^*{Gr}(k,n)$ is the cotangent bundle of the Grassmannian of $k$-planes of $n$-dimensional space. We
We consider the quantum difference equation of the Hilbert scheme of points in C2. This equation is the K-theoretic generalization of the quantum differential equation discovered by A. Okounkov and

## References

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• Mathematics
Symmetry, Integrability and Geometry: Methods and Applications
• 2019
Let $X$ be a holomorphic symplectic variety with a torus $\mathsf{T}$ action and a finite fixed point set of cardinality $k$. We assume that elliptic stable envelope exists for $X$. Let $A_{I,J}= • Mathematics Selecta Mathematica • 2019 In this paper we consider the cotangent bundles of partial flag varieties. We construct the $$K$$K-theoretic stable envelopes for them and also define a version of the elliptic stable envelopes. We • Mathematics International Mathematics Research Notices • 2022 Let$\textsf {X}$and$\textsf {X}^{!}$be a pair of symplectic varieties dual with respect to 3D mirror symmetry. The$K$-theoretic limit of the elliptic duality interface is an equivariant • P. Koroteev • Mathematics Communications in Mathematical Physics • 2021 We study quantum geometry of Nakajima quiver varieties of two different types—framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection Consider the$3$-dimensional$\mathcal N=4$supersymmetric gauge theory associated with a compact Lie group$G_c$and its quaternionic representation$\mathbf M\$. Physicists study its Coulomb branch,
In this paper, we explore a consequence of symplectic duality (also known as 3d mirror symmetry) in the setting of enumerative geometry. The theory of quasimaps allows one to associate hypergeometric
• Mathematics
Inventiones mathematicae
• 2022
For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the
Consider the 3-dimensional N = 4 supersymmetric gauge theory associated with a compact Lie group G and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompact
These are notes from my lectures on quantum K-theory of Nakajima quiver varieties and K-theoretic Donaldson-Thomas theory of threefolds given at Columbia and Park City Mathematics Institute. They