# Remarks on $A^{(1)}_n$ face weights

@article{Kuniba2017RemarksO, title={Remarks on \$A^\{(1)\}\_n\$ face weights}, author={Atsuo Kuniba}, journal={arXiv: Mathematical Physics}, year={2017} }

An elementary proof is given for the elliptic and trigonometric Boltzmann weights of the $A^{(1)}_n$ face model about their factorization at a special point of the spectral parameter and the sum-to-1 property. They generalize analogous results in the corresponding vertex model obtained recently.

## 2 Citations

### Stochasticization of Solutions to the Yang–Baxter Equation

- MathematicsAnnales Henri Poincaré
- 2019

In this paper, we introduce a procedure that, given a solution to the Yang–Baxter equation as input, produces a stochastic (or Markovian) solution to (a possibly dynamical version of) the Yang–Baxter…

### Stochasticization of Solutions to the Yang–Baxter Equation

- MathematicsAnnales Henri Poincaré
- 2019

In this paper, we introduce a procedure that, given a solution to the Yang–Baxter equation as input, produces a stochastic (or Markovian) solution to (a possibly dynamical version of) the Yang–Baxter…

## References

SHOWING 1-8 OF 8 REFERENCES

### An Algebraic Construction of Duality Functions for the Stochastic $${\mathcal{U}_q( A_n^{(1)})}$$Uq(An(1)) Vertex Model and Its Degenerations

- Mathematics
- 2018

A recent paper (Kuniba in Nucl Phys B 913:248–277, 2016) introduced the stochastic $${\mathcal{U}_q(A_n^{(1)})}$$Uq(An(1)) vertex model. The stochastic S-matrix is related to the R-matrix of the…

### Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities

- Mathematics
- 1984

AbstractThe eight-vertex model is equivalent to a “solid-on-solid” (SOS) model, in which an integer heightli is associated with each sitei of the square lattice. The Boltzmann weights of the model…

### Symmetric elliptic functions, IRF models, and dynamic exclusion processes

- Mathematics
- 2017

We introduce stochastic Interaction-Round-a-Face (IRF) models that are related to representations of the elliptic quantum group $E_{\tau,\eta}(sl_2)$. For stochasic IRF models in a quadrant, we…

### Exactly Solvable SOS Models II: Proof of the star-triangle relation and combinatorial identities

- Mathematics
- 1988

### Exactly solved models in statistical mechanics

- Physics
- 1982

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical…

### Symmetric tensors of the A (1) n−1 family

- Algebraic Analysis, 1
- 1988

### The A (1) n face models

- Commun. Math. Phys. 119
- 1989

### Stochastic R matrix for Uq(A (1) n )

- Nucl. Phys. B913
- 2016