## 89 Citations

### Homomorphisms between different quantum toroidal and affine Yangian algebras

- MathematicsJournal of Pure and Applied Algebra
- 2019

### A note on quiver quantum toroidal algebra

- MathematicsJournal of High Energy Physics
- 2022

Abstract
Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian $$ \mathfrak{gl} $$
gl
1. The characteristic feature…

### The Maulik–Okounkov R-matrix from the Ding–Iohara–Miki algebra

- Mathematics
- 2017

The integrability of 4d $${\mathcal{N}}=2$$ gauge theories has been explored in various contexts, e.g., the Seiberg–Witten curve and its quantization. Recently, Maulik and Okounkov proposed that an…

### Shalika germs for tamely ramified elements in $GL_n$

- Mathematics
- 2022

. Degenerating the action of the elliptic Hall algebra on the Fock space, we give a combinatorial formula for the Shalika germs of tamely ramiﬁed regular semisimple elements γ of GL n over a…

### Gluing two affine Yangians of 𝔤𝔩1

- MathematicsJournal of High Energy Physics
- 2019

Abstract
We construct a four-parameter family of affine Yangian algebras by gluing two copies of the affine Yangian of 𝔤𝔩1. Our construction allows for gluing operators with arbitrary (integer…

### q-deformation of corner vertex operator algebras by Miura transformation

- Mathematics
- 2021

Recently, Gaiotto and Rapcak proposed a generalization of WN algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as…

### Toroidal and elliptic quiver BPS algebras and beyond

- MathematicsJournal of High Energy Physics
- 2022

Abstract
The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce…

### Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds.

- Mathematics
- 2020

To a smooth local toric Calabi-Yau 3-fold $X$ we associate the Heisenberg double of the (equivariant spherical) Cohomological Hall algebra in the sense of Kontsevich and Soibelman. This Heisenberg…

### Shifted quiver Yangians and representations from BPS crystals

- Mathematics
- 2021

We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. We construct representations of the shifted…

### A note on the algebraic engineering of 4D N=2 super Yang–Mills theories

- MathematicsPhysics Letters B
- 2019

## References

SHOWING 1-10 OF 38 REFERENCES

### Limits of quantum toroidal and affine Yangian

- Mathematics
- 2016

In this short note, we compute the classical limits of the quantum toroidal and the affine Yangian algebras of sl(n) by generalizing our arguments for the case of gl(1) from arXiv:1404.5240. These…

### Homomorphisms between different quantum toroidal and affine Yangian algebras

- MathematicsJournal of Pure and Applied Algebra
- 2019

### Drinfeld realization of the elliptic Hall algebra

- Mathematics
- 2010

We give a new presentation of the Drinfeld double $\boldsymbol{\mathcal {E}}$ of the (spherical) elliptic Hall algebra $\boldsymbol{\mathcal{E}}^{+}$ introduced in our previous work (Burban and…

### Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2

- Mathematics
- 2012

We construct a representation of the affine W-algebra of ${\mathfrak{g}}{\mathfrak{l}}_{r}$ on the equivariant homology space of the moduli space of Ur-instantons, and we identify the corresponding…

### Quantum Groups and Quantum Cohomology

- Mathematics
- 2012

In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q,…

### Equivariant K-theory of Hilbert schemes via shuffle algebra

- Mathematics
- 2011

In this paper we construct the action of Ding-Iohara and shuffle algebras in the sum of localized equivariant K-groups of Hilbert schemes of points on C^2. We show that commutative elements K_i of…

### Quantum continuous gl ∞ : Semiinﬁnite construction of representations

- Mathematics
- 2011

We begin a study of the representation theory of quantum continuous gl ∞ , whichwedenoteby E .Thisalgebradependsontwoparametersandisadeformedversion of the enveloping algebra of the Lie algebra of…

### A commutative algebra on degenerate CP^1 and Macdonald polynomials

- Mathematics
- 2009

We introduce a unital associative algebra A over degenerate CP^1. We show that A is a commutative algebra and whose Poincar'e series is given by the number of partitions. Thereby we can regard A as a…

### On the Hall algebra of an elliptic curve, I

- Mathematics
- 2005

This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to…

### Quantum affine algebras

- Mathematics
- 1991

AbstractWe classify the finite-dimensional irreducible representations of the quantum affine algebra
$$U_q (\hat sl_2 )$$
in terms of highest weights (this result has a straightforward…