Category O for quantum loop algebras
Representation Theory
2025-09-17 v3 Quantum Algebra
Abstract
We generalize the Hernandez-Jimbo category O of representations of Borel subalgebras of quantum affine algebras to the case of quantum loop algebras for arbitrary Kac-Moody g (as well as related algebras, such as quantum toroidal gl_1). Moreover, we give explicit realizations of all simple modules, and devise tools for the computation of q-characters that are new even for g of finite type. Our techniques allow us to generalize classic results of Frenkel-Hernandez, Frenkel-Mukhin, Hernandez-Jimbo and Hernandez-Leclerc, as well as prove conjectures of Feigin-Jimbo-Miwa-Mukhin and Mukhin-Young.
Cite
@article{arxiv.2501.00724,
title = {Category O for quantum loop algebras},
author = {Andrei Neguţ},
journal= {arXiv preprint arXiv:2501.00724},
year = {2025}
}