• Corpus ID: 12125191

A GEOMETRIC BOSON-FERMION CORRESPONDENCE

@article{Savage2005AGB,
  title={A GEOMETRIC BOSON-FERMION CORRESPONDENCE},
  author={Alistair Savage},
  journal={arXiv: Representation Theory},
  year={2005}
}
  • Alistair Savage
  • Published 23 August 2005
  • Mathematics
  • arXiv: Representation Theory
The fixed points of a natural torus action on the Hilbert schemes of points in C 2 are quiver varieties of type A1. The equivariant cohomology of the Hilbert schemes and quiver varieties can be given the structure of bosonic and fermionic Fock spaces respectively. Then the local- ization theorem, which relates the equivariant cohomology of a space with that of its fixed point set, yields a geometric realization of the important boson-fermion correspondence. R´´ Les points fixes d'une action… 
View PDF on arXiv
10 Citations
Background Citations
1
Results Citations
2

Figures from this paper

10 Citations

The double of representations of Cohomological Hall algebras

Given a quiver Q with/without potential, one can construct an algebra structure on the cohomology of the moduli stacks of representations of Q. The algebra is called Cohomological Hall algebra (COHA…

Categorical Bernstein operators and the Boson-Fermion correspondence

We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to infinite chain…

Torsion-free Sheaves on C P 2 and Representations of the Affine Lie Algebra ĝl ( r ) March 1 , 2022

  • Mathematics
  • 2022
We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP . Using these…

The combinatorics ofC⁎-fixed points in generalized Calogero-Moser spaces and Hilbert schemes

The combinatorics of $\mathbb{C}^*$-fixed points in generalized Calogero-Moser spaces and Hilbert schemes.

In this paper we study the combinatorial consequences of the relationship between rational Cherednik algebras of type $G(l,1,n)$, cyclic quiver varieties and Hilbert schemes. We classify and…

Categorical Bernstein operators and the Boson-Fermion correspondence

We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to infinite chain…

An equivalence between truncations of categorified quantum groups and Heisenberg categories

We introduce a simple diagrammatic 2-category $\mathscr{A}$ that categorifies the image of the Fock space representation of the Heisenberg algebra and the basic representation of…

Framed torsion-free sheaves on CP2, Hilbert schemes, and representations of infinite dimensional Lie algebras

Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves

We define complexes of vector bundles on products of moduli spaces of framed rank r torsion-free sheaves on $${\mathbb{P}^2}$$ . The top non-vanishing equivariant Chern classes of the cohomology of…

Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)}

We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP^2. Using these…

References

SHOWING 1-10 OF 26 REFERENCES

Instantons and affine algebras I: The Hilbert scheme and vertex operators

This is the first in a series of papers which describe the action of an affine Lie algebra with central charge $n$ on the moduli space of $U(n)$-instantons on a four manifold $X$. This generalises…

Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras

To Professor Shoshichi Kobayashi on his 60th birthday 1. Introduction. In this paper we shall introduce a new family of varieties, which we call quiver varieties, and study their geometric…

Bases of Representations of Type A Affine Lie Algebras via Quiver Varieties and Statistical Mechanics

We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are…

Jack polynomials and Hilbert schemes of points on surfaces

The Jack symmetric polynomials $P_\lambda^{(\alpha)}$ form a class of symmetric polynomials which are indexed by a partition $\lambda$ and depend rationally on a parameter $\alpha$. They reduced to…

Lectures on Hilbert schemes of points on surfaces

Introduction Hilbert scheme of points Framed moduli space of torsion free sheaves on $\mathbb{P}^2$ Hyper-Kahler metric on $(\mathbb{C}^2)^{[n]}$ Resolution of simple singularities Poincare…

A geometric realization of spin representations and Young diagrams from quiver varieties

Quivers, perverse sheaves, and quantized enveloping algebras

1. Preliminaries 2. A class of perverse sheaves on Ev 3. Multiplication 4. Restriction 5. Fourier-Deligne transform 6. Analysis of a sink 7. Multiplicative generators 8. Compatibility of…

On the homology of the Hilbert scheme of points in the plane

Geir Ellingsrud 1 and Stein Arild Stromme 2 i Matematisk institutt, Universitetet i Oslo, Blindern, N-Oslo 3, Norway 2 Matematisk institutt, Universitetet i Bergen, N-5014 Bergen, Norway Although…

Transformation Groups for Soliton Equations —Euclidean Lie Algebras and Reduction of the KP Hierarchy—

This is the last chapter of our series of papers [1], [3], [10], [11] on transformation groups for soliton equations. In [1] a link between the KdV (Korteweg de Vries) equation and the affine Lie…

Quiver varieties and Hilbert schemes

In this note we give an explicit geometric description of some of the Nakajima's quiver varieties. More precisely, we show that the $\Gamma$-equivariant Hilbert scheme $X^{\Gamma[n]}$ and the Hilbert…