Boundary state of a $U_q\left(\widehat{gl}\right(N|N\left)\right)$ analogue of the half-infinite t − J model

A $U_q\left(\widehat{gl}\right(N|N\left)\right)$-analogue of the half-infinite t  −  J model with a boundary is studied by using the vertex operator approach. We find an explicit bosonic formula of the boundary state in the integrable highest-weight module over the quantum superalgebra $U_q\left(\widehat{gl}\right(N|N\left)\right)$. (paper: quantum statistical physics, condensed matter, integrable systems)