ar X iv : m at h / 02 05 33 5 v 1 [ m at h . Q A ] 3 1 M ay 2 00 2 Yang - Baxter maps and integrable dynamics

ar X iv : m at h / 02 08 04 3 v 1 [ m at h . Q A ] 6 A ug 2 00 2 QUANTUM AFFINE

Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection algebras of type d (1) n to determine new n-parameter families of non-diagonal reflection matrices. These matrices describe the reflection of vector solitons off t...

ar X iv : m at h / 05 02 57 3 v 6 [ m at h . A G ] 1 4 M ay 2 00 6 ON DEFORMATIONS OF FLAG

Any (global) deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 02 10 26 0 v 2 [ m at h . Q A ] 1 4 N ov 2 00 2 On representations of braid groups determined by directed graphs

We prove that any non L-cocommutative finite Markov L-coalgebra yields at least two solutions of the Yang-Baxter equation and therefore at least two representations of the braid groups. We conclude by a generalisation of these constructions to any coalgebra.

ar X iv : q ua nt - p h / 02 05 05 2 v 1 1 0 M ay 2 00 2 ALTERNATIVE STRUCTURES AND BIHAMILTONIAN SYSTEMS

In the study of bi-Hamiltonian systems (both classical and quantum) one starts with a given dynamics and looks for all alternative Hamiltonian descriptions it admits. In this paper we start with two compatible Hermitian structures (the quantum analog of two compatible classical Poisson brackets) and look for all the dynamical systems which turn out to be bi-Hamiltonian with respect to them.