N. Crampe

General boundary conditions for the sl(N) and sl(M|N) open spin chains

Two types of boundary conditions (soliton preserving and soliton non-preserving) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the soliton preserving case is worked out. The connection between the soliton non-preserving boundary conditions and the twisted (super-) Yangians is also discussed.Two types of boundary conditions (soliton preserving and soliton non-preserving) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the soliton preserving case is worked out. The connection between the soliton non-preserving boundary conditions and the twisted (super-) Yangians is also discussed.

R-matrix presentation for super-Yangians Y(osp(m|2n))

We give a RTT presentation of super-Yangians Y(g) for g=osp(m|2n), thereby unifying the formalism with the cases of g=so(n) and g=sp(2n).

Classification of reflection matrices related to (super-)Yangians and application to open spin chain models

We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe ansatz resolution for the so(m) and sp(n) open spin chains with boundary conditions described by the diagonal solutions.

Bethe Ansatz equations and exact S matrices for the osp(M |2n) open super spin chain.

Abstract We formulate the Bethe ansatz equations for the open super-spin chain based on the super Yangian of osp ( M |2 n ) and with diagonal boundary conditions. We then study the bulk and boundary scattering of the osp (1|2 n ) open spin chain.

Super Yangian Y(osp(1|2)) and the Universal R-matrix of Its Quantum Double

We present the Drinfeld realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary Serre relations. The construction of its quantum double is carried out. This allows us to give the universal R-matrix of DY(osp(1|2)).

Hopf structure of the Yangian Y(sln) in the Drinfel’d realization

The Yangian of the Lie algebra sln is known to have different presentations, in particular the RTT realization and the Drinfel’d realization. Using the isomorphism between them, the explicit expressions of the comultiplication, the antipode and the counit in the Drinfel’d realization of the Yangian Y(sln) are given. As examples, the cases of Y(sl2) and Y(sl3) are worked out.

3-state Hamiltonians associated to solvable 33-vertex models

Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang–Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.

General boundary conditions for the sl({\cal N}) and sl({\cal M}|{\cal N}) open spin chains

Two types of boundary conditions (soliton preserving and soliton non-preserving) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the soliton preserving case is worked out. The connection between the soliton non-preserving boundary conditions and the twisted (super-) Yangians is also discussed.Two types of boundary conditions (soliton preserving and soliton non-preserving) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the soliton preserving case is worked out. The connection between the soliton non-preserving boundary conditions and the twisted (super-) Yangians is also discussed.

General boundary conditions for the and open spin chains

Two types of boundary conditions (soliton preserving and soliton non-preserving) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the soliton preserving case is worked out. The connection between the soliton non-preserving boundary conditions and the twisted (super-) Yangians is also discussed.Two types of boundary conditions (soliton preserving and soliton non-preserving) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the soliton preserving case is worked out. The connection between the soliton non-preserving boundary conditions and the twisted (super-) Yangians is also discussed.