Title: Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model,
Abstract: The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin
chain, of arbitrary spin-$s$, in the case, when both reflection matrices have
the upper-triangular form is analyzed. The general form of the Bethe vectors is
studied. In the particular form, Bethe vectors admit the recurrent procedure,
with an appropriate modification, used previously in the case of the XXX
Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple
expression for the off-shell action of the transfer matrix of the chain as well
as the spectrum of the transfer matrix and the corresponding Bethe equations.
As in the XXX case, the so-called quasi-classical limit gives the off-shell
action of the generating function of the corresponding trigonometric Gaudin
Hamiltonians with boundary terms.