# A note on quiver Yangians and ℛ-matrices

@article{Bao2022ANO, title={A note on quiver Yangians and ℛ-matrices}, author={Jiakang Bao}, journal={Journal of High Energy Physics}, year={2022}, volume={2022}, pages={1-46} }

In this note, we study possible ℛ-matrix constructions in the context of quiver Yangians and Yang-Baxter algebras. For generalized conifolds, We also discuss the relations between the quiver Yangians and some other Yangian algebras (and W $$ \mathcal{W} $$ -algebras) in literature.

## 5 Citations

### Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds

- Mathematics
- 2022

We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach in literature. We also prove that the quiver Yangians related…

### Gauge/Bethe correspondence from quiver BPS algebras

- MathematicsJournal of High Energy Physics
- 2022

We study the Gauge/Bethe correspondence for two-dimensional N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

### BPS States Meet Generalized Cohomology

- Mathematics
- 2023

In this note we review a construction of a BPS Hilbert space in an effective supersymmetric quiver theory with 4 supercharges. We argue abstractly that this space contains elements of an equivariant…

### A Survey of Toric Quivers and BPS Algebras

- Mathematics
- 2023

In this note, we discuss some properties of the quiver BPS algebras. We consider how they would transform under different operations on the toric quivers, such as dualities and higgsing. We also give…

### Mahler Measuring the Genetic Code of Amoebae

- Mathematics
- 2022

Amoebae from tropical geometry and the Mahler measure from number theory play important roles in quiver gauge theories and dimer models. Their dependencies on the coeﬃcients of the Newton polynomial…

## References

SHOWING 1-10 OF 76 REFERENCES

### Instanton R-matrix and W-symmetry

- Mathematics
- 2019

We study the relation between W1+∞ algebra and Arbesfeld-SchiffmannTsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation.…

### Gauge/Bethe correspondence from quiver BPS algebras

- MathematicsJournal of High Energy Physics
- 2022

We study the Gauge/Bethe correspondence for two-dimensional N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

### Liouville reflection operator, affine Yangian and Bethe ansatz

- MathematicsJournal of High Energy Physics
- 2020

In these notes we study integrable structure of conformal field theory by means of Liouville reflection operator/Maulik Okounkov R-matrix. We discuss relation between RLL and current realization of…

### Quiver Yangian from crystal melting

- MathematicsJournal of High Energy Physics
- 2020

We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau…

### Affine super Yangians and rectangular W-superalgebras

- MathematicsJournal of Mathematical Physics
- 2022

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian [Formula: see text] to the universal enveloping algebra of the rectangular…

### Affine Super Yangian

- Mathematics
- 2019

In this paper, we define the affine super Yangian $Y_{\varepsilon_1,\varepsilon_2}(\widehat{\mathfrak{sl}}(m|n))$ with a coproduct structure. We also obtain an evaluation homomorphism, that is, an…

### W$$ \mathcal{W} $$ -algebra modules, free fields, and Gukov-Witten defects

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe study the structure of modules of corner vertex operator algebras arrising at junctions of interfaces in N=4$$ \mathcal{N}=4 $$ SYM. In most of the paper, we concentrate on truncations of…

### 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,…

### Webs of W-algebras

- MathematicsJournal of High Energy Physics
- 2018

A bstractWe associate vertex operator algebras to (p, q)-webs of interfaces in the topologically twisted N=4$$ \mathcal{N}=4 $$ super Yang-Mills theory. Y-algebras associated to trivalent junctions…