The half-infinite XXZ open spin chain with general integrable boundary
conditions is considered within the recently developed `Onsager's approach'.
Inspired by the finite size case, for any type of integrable boundary
conditions it is shown that the transfer matrix is simply expressed in terms of
the elements of a new type of current algebra recently introduced. In the
massive regime −1<q<0, level one infinite dimensional representation
(q−vertex operators) of the new current algebra are constructed in order to
diagonalize the transfer matrix. For diagonal boundary conditions, known
results of Jimbo {\it et al.} are recovered. For upper (or lower) non-diagonal
boundary conditions, a solution is proposed. Vacuum and excited states are
formulated within the representation theory of the current algebra using
q−bosons, opening the way for the calculation of integral representations of
correlation functions for a non-diagonal boundary. Finally, for q generic the
long standing question of the hidden non-Abelian symmetry of the Hamiltonian is
solved: it is either associated with the q−Onsager algebra (generic
non-diagonal case) or the augmented q−Onsager algebra (generic diagonal
case).Comment: 28 pages; Presentation improved; misprints corrected; to appear in
Nucl. Phys.
