Quantum loop symmetric pairs and meromorphic abelian K-matrices

Let g be a symmetrizable Kac--Moody algebra, let q^× not be a root of unity, and let U=Uq(Lg) be the corresponding quantum loop algebra, equipped with Hernandez' deformed Drinfeld coproduct. For every diagram involution $τ$ of g, we introduce a coideal subalgebra B in a topological completion of U, obtained by adapting the Letzter-Kolb construction of quantum symmetric pairs to the Drinfeld generators of U. We derive necessary constraints on the parameters defining B from a minimality condition on its intersection with the quantum loop Cartan subalgebra U⁰. We show that B yields a topological realization of the quasi-split quantum loop group U^ associated with $τ$, in the presentation recently obtained by Lu-Pan, building on work of Chen-Lu-Pan-Ruan-Wang on Hopf algebras. By pullback, this gives rise to a rational restriction functor on category O representations. For modules with rational weights and generic values of the spectral parameter, every U^-submodule of a restricted module is stable under the derived quantum loop algebra U'. In particular, irreducibility is generically preserved under restriction for such modules. For |q|≠1 and under explicit assumptions on the quantum Cartan matrix, we construct meromorphic abelian K-matrices whose tensor counterparts yield boundary q-characters for both U-modules and U^-modules. Finally, we extend the coideal construction and Drinfeld coaction to shifted quantum loop algebras with arbitrary coweight shifts, providing a new approach to GKLO representations by restriction from ordinary shifted quantum loop algebras.