## 80 Citations

Cohomology of a flag variety as a Bethe algebra

- Mathematics
- 2011

We interpret the equivariant cohomology $H_{GL_n }^* $(ℱλ,ℂ) of a partial flag variety ℱλ parametrizing chains of subspaces 0 = F0 ⊂ F1 ⊂ … ⊂ FN = ℂn, dimFi/Fi−1 = λi, as the Bethe algebra of the…

Equivariant quantum cohomology and the geometric Satake equivalence

- Mathematics
- 2016

Recent work on equivariant aspects of mirror
symmetry has discovered relations between the equivariant quantum
cohomology of symplectic resolutions and Casimir-type connections
(among many other…

Quantum Cohomology of Hypertoric Varieties and Geometric Representations of Yangians

- Mathematics
- 2013

This thesis compares two geometric constructions of a Yangian, due to Varagnolo and Nakajima on the one hand and Maulik and Okounkov on the other. It also, separately, computes the quantum cohomology…

QUANTUM D-MODULES OF TORIC VARIETIES AND OSCILLATORY INTEGRALS

- Mathematics
- 2019

We review mirror symmetry for the quantum cohomology D-module of a compact weak-Fano toric manifold. We also discuss the relationship to the GKZ system, the Stanley-Reisner ring, the Mellin-Barnes…

Seminar on Quantum Groups & Quantum Cohomology of Symplectic Varieties

- Mathematics
- 2020

More generally, the cohomology of X is determined by the cohomology of XT together with the restriction maps on cohomology, given that the cohomology is taken equivariantly with respect to the torus…

Slodowy slices and universal Poisson deformations

- MathematicsCompositio Mathematica
- 2011

Abstract We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre.…

Quantum K-theory of quiver varieties and many-body systems

- MathematicsSelecta Mathematica
- 2021

We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider…

Intersection cohomology and quantum cohomology of conical symplectic resolutions

- Mathematics
- 2015

For any conical symplectic resolution, we give a conjecture relating the intersection cohomology of the singular cone to the quantum cohomology of its resolution. We prove this conjecture for…

A mirror construction for the big equivariant quantum cohomology of toric manifolds

- Mathematics
- 2015

We identify a certain universal Landau–Ginzburg model as a mirror of the big equivariant quantum cohomology of a (not necessarily compact or semipositive) toric manifold. The mirror map and the…

Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety

- Mathematics
- 2013

We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a $$\mathfrak{g}\mathfrak{l}_n$$ partial flag variety. These hypergeometric solutions manifest the…

## References

SHOWING 1-10 OF 47 REFERENCES

Equivariant quantum cohomology of homogeneous spaces.

- Mathematics
- 2005

We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X=G/P. As in the case when X is a Grassmannian, studied by the author in a…

A Mirror Symmetric Construction of Qh

- Mathematics
- 2007

Let G be a simple simply connected complex algebraic group. We give a Lie-theoretic construction of a conjectural mirror family associated to a general flag variety G/P, and show that it recovers the…

Root Systems and the Quantum Cohomology of ADE resolutions

- Mathematics
- 2007

We compute the C*-equivariant quantum cohomology ring of Y, the minimal resolution of the DuVal singularity C^2/G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of…

QUANTUM COHOMOLOGY OF FLAG MANIFOLDS

- Mathematics
- 1993

We discuss relations of Vafa’s quantum cohomology with Floer’s homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of…

Quantum cohomology of flag manifolds and Toda lattices

- Mathematics
- 1993

We discuss relations of Vafa's quantum cohomology with Floer's homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of…

Quantum cohomology of the Hilbert scheme of points in the plane

- Mathematics
- 2004

We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points of ℂ2. The operator of quantum multiplication by the divisor class is a nonstationary deformation…

A Kohno-Drinfeld theorem for quantum Weyl groups

- Mathematics
- 2000

Let g be a complex, simple Lie algebra and t a Cartan subalgebra of g. A new unitary, flat connection on t with values in any finite-dimensional g-module V and simple poles along the root hyperplanes…

Quiver Varieties and Yangians

- Mathematics
- 2000

We prove a conjecture of Nakajima (for type A it was announced by Ginzburg and Vasserot) giving a geometric realization, via quiver varieties, of the Yangian of type ADE (and more in general of the…

Cohomology of the Minimal Nilpotent Orbit

- Mathematics
- 2007

We compute the integral cohomology of the minimal nontrivial nilpotent orbit in a complex simple (or quasi-simple) Lie algebra. We find by a uniform approach that the middle cohomology group is…