Spin excitations in the integrable open quantum group invariant supersymmetric t-J model

The integrable quantum group $spl_q(2,1)$-invariant supersymmetric t-J model with open boundaries is studied via an analytic treatment of the Bethe equations. An $su(2)$ feature is seen to hold for states at or close to half-filling. For these states the eigenvalues of the transfer matrix of the t-J model satisfy a set of $su(2)$ functional relations. The finite-size corrections to the relevant eigenvalues, and thus the surface effect on the spin excitations, have been calculated analytically by solving the functional relations.