# MacMahon KZ equation for Ding-Iohara-Miki algebra

@article{Cheewaphutthisakun2021MacMahonKE, title={MacMahon KZ equation for Ding-Iohara-Miki algebra}, author={Panupong Cheewaphutthisakun and Hiroaki Kanno}, journal={Journal of High Energy Physics}, year={2021} }

Abstract
We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of the intertwiners of the vector and the MacMahon representations of Ding-Iohara-Miki algebra. These intertwiners are cousins of the refined topological vertex which is regarded as the intertwining operator of the Fock representation. The shift of the spectral parameter of the intertwiners is generated by the operator which is constructed from the universal R matrix. The solutions to the generalized…

## 3 Citations

### Quasi-Hopf twist and elliptic Nekrasov factor

- MathematicsJournal of High Energy Physics
- 2021

Abstract
We investigate the quasi-Hopf twist of the quantum toroidal algebra of $$ {\mathfrak{gl}}_1 $$
gl
1
as an elliptic deformation. Under the quasi-Hopf twist the underlying algebra…

### Shifted quiver quantum toroidal algebra and subcrystal representations

- MathematicsJournal of High Energy Physics
- 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…

### The R-matrix of the quantum toroidal algebra

- Mathematics
- 2020

We consider the R–matrix of the quantum toroidal algebra of type gl1, both abstractly and in Fock space representations. We provide a survey of a certain point of view on this object which involves…

## References

SHOWING 1-10 OF 64 REFERENCES

### Quantum continuous gl∞: Semi-infinite construction of representations

- Kyoto J. Math. 51
- 2011

### Mixed network calculus, arXiv:2012.15563

- 2012

### A q

- Mathematics, Philosophy

. We prove that for integers q > 1 ,m ≥ 1 and positive rationals r 1 ,r 2 , ··· ,r m (cid:54) = q j ,j = 1 , 2 , ··· , the series ∞ (cid:88) j =1 q − 1 − ) ··· q − j r m ) is irrational. Furthermore,…

### Quantum toroidal gl1-algebra: Plane partitions

- Mathematics
- 2012

In this, the third paper of the series, we construct a large family of representations of the quantum toroidal gl1-algebra whose bases are parameterized by plane partitions with various boundary…

### The R-matrix of the quantum toroidal algebra

- Mathematics
- 2020

We consider the R-matrix of the quantum toroidal algebra of type gl_1, both abstractly and in Fock space representations. We provide a survey of a certain point of view on this object which involves…

### The R-matrix of the quantum toroidal algebra

- Mathematics
- 2020

We consider the R–matrix of the quantum toroidal algebra of type gl1, both abstractly and in Fock space representations. We provide a survey of a certain point of view on this object which involves…

### Non-Stationary Ruijsenaars Functions for κ=t−1/N and Intertwining Operators of Ding-Iohara-Miki Algebra

- Mathematics
- 2020

We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case $\kappa=t^{-1/N}$, using the intertwining operators of the Ding-Iohara-Miki…

### Localization of 4d $$ \mathcal{N} $$ = 1 theories on 𝔻2× 𝕋2

- Mathematics
- 2019

We consider 4d $$ \mathcal{N} $$ = 1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological…

### Localization of 4 d N = 1 theories on D 2 × T 2

- Mathematics
- 2019

We consider 4d N = 1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of…