We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the
case when both boundary matrices can be brought to the upper-triangular form. We define …

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the
case, when both reflection matrices have the upper-triangular form is analyzed. The general …

Let $\mathfrak {g} $ be a complex simple Lie algebra and $ U_q\hat {\mathfrak {g}} $ the
corresponding quantum affine algebra. We prove that every irreducible finite-dimensional …

Statistical physics aims to study macroscopic systems from the microscopic properties of its
constituents. It originates from the kinetic theory of gases, a theory that was born in the …

2 and diagonal boundary magnetic fields that depend on a parameter x is studied. For real
x> 0, the exact finite-size ground-state eigenvalue of the spin-chain Hamiltonian is explicitly …

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and
real forms of complex Lie algebras, and are wellstudied in the context of symmetrizable Kac …

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of
groundbreaking contributions in several fields, including representation theory, integrable …

Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …

We classify trigonometric reflection matrices for vector representation of quasistandard
quantum affine Kac-Moody pairs of classical Lie type. The coideal subalgebras involved are …