# A GEOMETRIC BOSON-FERMION CORRESPONDENCE

@article{Savage2005AGB, title={A GEOMETRIC BOSON-FERMION CORRESPONDENCE}, author={Alistair Savage}, journal={arXiv: Representation Theory}, year={2005} }

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…

## 10 Citations

### The double of representations of Cohomological Hall algebras

- Mathematics
- 2016

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

- MathematicsSelecta Mathematica
- 2020

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

- MathematicsJournal of Algebra
- 2020

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

- Mathematics
- 2016

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

- Materials ScienceSelecta Mathematica
- 2020

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

- Mathematics
- 2017

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

- Mathematics
- 2011

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

- Mathematics
- 2010

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)}

- Mathematics
- 2006

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…

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