In this talk, I present a ring isomorphism between ``$t$-
deformed'' Grothendieck rings (=quantum Grothendieck rings) of finite-
dimensional module categories of quantum affine algebras of type $\
mathrm{A}_{2n-1}^{(1)}$ and $\mathrm{B}_n^{(1)}$. This isomorphism
implies several new positivity properties of $(q, t)$-characters of
simple modules of type $\mathrm{B}_n^{(1)}$. Moreover, it specializes at
$t = 1$ to the isomorphism between usual Grothendieck rings obtained by
Kashiwara, Kim and Oh via generalized quantum affine Schur-Weyl
dualities. This coincidence gives an affirmative answer to Hernandez's
conjecture (2002) for type $\mathrm{B}_n^{(1)}$ : the $(q, t)$-
characters of simple modules specialize to their actual $q$-characters.
Hence, in this case, the multiplicities of simple modules in standard
modules are given by the evaluation of certain analogues of Kazhdan-
Lusztig polynomials whose coefficients are positive. If time permits, we
discuss a refinement of description of our isomorphism.

This talk is based on a joint work with David Hernandez.