Publication

Category O for quantum loop algebras

2026

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 𝔤𝔩1). 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 and Hernandez, Frenkel and Mukhin, Hernandez and Jimbo, and Hernandez and Leclerc, as well as prove conjectures of Feigin, Jimbo, Miwa, and Mukhin, and Mukhin and Young.

Official source

https://infoscience.epfl.ch/entities/publication/6ee876d4-2c8a-4560-bcea-e6a0bed29bcc

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6ee876d4-2c8a-4560-bcea-e6a0bed29bcc

About this result

Related concepts (32)

Quantum group

In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. Despite their name, they do not themselves have a natural group structure, though they are in some sense 'close' to a group.

Simple module

In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero proper submodules. Equivalently, a module M is simple if and only if every cyclic submodule generated by a non-zero element of M equals M. Simple modules form building blocks for the modules of finite length, and they are analogous to the simple groups in group theory. In this article, all modules will be assumed to be right unital modules over a ring R.

Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a ) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the , whose objects are sets and whose arrows are functions. is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent.

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