Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system

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