Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category
O
\mathcal {O}
of the Borel subalgebra of an arbitrary untwisted quantum affine algebra. Our representation-theoretical construction is based on the study of the action of Cartan-Drinfeld subalgebras. We prove the algebraic stable maps are invertible and depend rationally on the spectral parameter. As an application, we obtain new
R
R
-matrices in the category
O
\mathcal {O}
and we establish that a large family of simple modules, including the prefundamental representations associated to
Q
Q
-operators, generically commute as representations of the Cartan-Drinfeld subalgebra. We also establish categorified
Q
Q
∗
QQ^*
-systems in terms of the
R
R
-matrices we construct.