  It is known that there is a correspondence between representations of
superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of
correspondence between the twisted quantum affine superalgebra
$U_{q}(gl(2r|1)^{(2)})$ and the non-twisted quantum affine algebra
$U_{q}(so(2r+1)^{(1)})$, we proposed, in the previous paper [arXiv:1109.5524],
a Wronskian solution of the T-system for $U_{q}(so(2r+1)^{(1)})$ as a reduction
(folding) of the Wronskian solution for the non-twisted quantum affine
superalgebra $U_{q}(gl(2r|1)^{(1)})$. In this paper, we elaborate on this
solution, and give a proof missing in [arXiv:1109.5524]. In particular, we
explain its connection to the Cherednik-Bazhanov-Reshetikhin (quantum
Jacobi-Trudi) type determinant solution known in [arXiv:hep-th/9506167]. We
also propose Wronskian-type expressions of T-functions (eigenvalues of transfer
matrices) labeled by non-rectangular Young diagrams, which are quantum affine
algebra analogues of the Weyl character formula for $so(2r+1)$. We show that
T-functions for spinorial representations of $U_{q}(so(2r+1)^{(1)})$ are
related to reductions of T-functions for asymptotic typical representations of
$U_{q}(gl(2r|1)^{(1)})$.
