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Bo-yu Hou

Publications and source records attributed to Bo-yu Hou.

At least 19 recordsLinked to original sources
arXiv2003

Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_n)$ and its applications

We study the tensor product of the {\it higher spin representations} (see the definition in Sect. 2.2) of the elliptic quantum group $E_{τ,η}(sl_n)$. The transfer matrices associated with the $E_{τ,η}(sl_n)$-module are exactly diagonalized by the nested Bethe ansatz method. Some special cases of the construction give the exact solution for the $Z_n$ Belavin model and for the elliptic $A_{n-1}$ Ruijsenaars-Schneider model.

hep-th↗
arXiv2001

The Dn Ruijsenaars-Schneider model

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears as a natural degeneration and the nonrelativistic limit exactly leads to the well-known Calogero-Moser system associated with Dn Lie algebra.

hep-th↗
arXiv2001

The Lax pair for C_2-type Ruijsenaars-Schneider model

We study the C_2 Ruijsenaars-Schneider(RS) model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameter are constructed. Also given are the involutive Hamiltonians for the system. Taking nonrelativistic limit, we obtain the Lax pair of C_2 Calogero-Moser model.

hep-th↗
arXiv2001

The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves

We study the elliptic C_n and BC_n Ruijsenaars-Schneider models which is elliptic generalization of system given in hep-th/0006004. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the systems corresponding to Calogero-Moser and Toda types.

hep-th↗
arXiv2000

Integrability of the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider models

We study the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider(RS) models with interaction potential of trigonometric and rational types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking nonrelativistic limit, we also obtain the Lax pairs for the corresponding Calogero-Moser systems.

hep-th↗
arXiv1999

The general crossing relation for boundary reflection matrix

In this paper, we give the general crossing relation for boundary reflection matrix $R(β)$, which is the extension of the work given by Ghoshal and Zamolodchikov .We also use the first non-trivial extended crossing relation to determine the scaler factor of $R(β)$ which is the rational diagonal solution to the boundary Yang-Baxter equation in the case of l=2 and n=3.

hep-th↗
arXiv1998

The nondynamical r-matrix structure of the elliptic Ruijsenaars-Schneider model with N=2

We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider model with N=2 admits a nondynamical r-matrix structure and the corresponding classical r-matrix is the same as that of its non-relativistic counterpart (Calogero-Moser model) in the same gauge.The relation between our (classical)Lax operator and the Lax operator given by Ruijsenaars is also obtained.

solv-int↗
arXiv1997

The nondynamical r-matrix structure for the elliptic $A_{n-1}$ Calogero-Moser model

In this paper, we construct a new Lax operator for the elliptic $A_{n-1}$ Calogero-Moser model with general $n(2\leq n$) from the classical dynamical twisting,in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix structure of this Lax operator is obtained, which is elliptic $Z_n$-symmetric r-matrix.

q-alg↗
arXiv1997

The elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ and its bosonization at level one

We extend the work of Foda et al and propose an elliptic quantum algebra $A_{q,p}(\hat {sl_n})$. Similar to the case of $A_{q,p}(\hat {sl_2})$, our presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and $R^*$ are $Z_n$ symmetric R-matrices with the elliptic moduli chosen differently and a factor is also involved. With the help of the results obtained by Asai et al, we realize type I and type II vertex operators in terms of bosonic free fields for $Z_n$ symmetric Belavin model. We also give a bosonization for the elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ at level one.

hep-th↗