# Shifted quiver quantum toroidal algebra and subcrystal representations

@article{Noshita2022ShiftedQQ, title={Shifted quiver quantum toroidal algebra and subcrystal representations}, author={Go Noshita and Akimi Watanabe}, journal={Journal of High Energy Physics}, year={2022} }

Abstract
Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In particular, shifted QY acts on general subcrystals of the original BPS crystal. A trigonometric deformation called quiver quantum toroidal algebra (QQTA) was also proposed and shown to act on the same BPS crystal. Unlike QY, QQTA has a formal Hopf superalgebra structure which is useful in deriving…

## 6 Citations

### 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…

### Shifted quantum groups and matter multiplets in supersymmetric gauge theories

- Mathematics
- 2022

The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modiﬁcation of the original deﬁnition brings more ﬂexibility in the representation theory…

### Crystal melting, BPS quivers and plethystics

- MathematicsJournal of High Energy Physics
- 2022

Abstract
We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples.…

### 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…

### 5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$

- Mathematics
- 2022

We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition…

### Quiver Yangians and Crystal Melting: A Concise Summary

- Mathematics
- 2022

The goal of this short article is to summarize some of the recent developments in the quiver Yangians and crystal meltings. This article is based on a lecture delivered by the author at International…

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