The category of finite-dimensional representations of a quantum affine algebras is generically braided, in particular there
exist intertwiners \(V\otimes W\rightarrow W\otimes V\) for generic simple representations (these intertwiners are called R-matrices).
In simply-laced cases, Maulik-Okounkov proposed a geometric construction of R-matrices as composition of their
stable maps obtained from Nakajima quiver varieties.
After having reviewed these subjects, we will explain how by analogy one can construct stable maps on tensor products of
representations in the category O of the Borel subalgebra of an untwisted quantum affine algebra. The construction is based
on the study of the action of the Drinfeld-Cartan subalgebra. As an application, we obtain new R-matrices in the category O.
This is a part of the workshop on intertwining operators and R-matrices.