Category O for Quantum Loop Algebras of Kac-Moody Type
A representation-theoretic framework extending the Hernandez-Jimbo category O from Borel subalgebras of quantum affine algebras to quantum loop algebras of an arbitrary Kac-Moody algebra, and to related algebras such as quantum toroidal gl1. It provides explicit, uniform realizations of the underlying vector spaces of all simple modules indexed by rational l-weights, together with new techniques for computing q-characters that apply even in finite type, unifying and generalizing classical results in the theory.
2501.00724
This paper builds a category O of representations for quantum loop algebras attached to an arbitrary Kac-Moody Lie algebra, extending the Hernandez-Jimbo category O previously defined only for Borel …