English

The algebra $U_q(\hat{sl}_\infty)$ and applications

Quantum Algebra 2011-03-08 v2 Representation Theory

Abstract

In this note we consider the algebra Uq(sl^)U_q(\hat{sl}_\infty) and we study the category O of its integrable representations. The main motivations are applications to quantum toroidal algebras, more precisely predictions of character formulae for representations of quantum toroidal algebras. In this context, we state a general positivity conjecture for representations of Uq(sl^)U_q(\hat{sl}_\infty) viewed as representations of quantum toroidal algebras, that we prove for Kirillov-Reshetikhin modules.

Keywords

Cite

@article{arxiv.1001.3047,
  title  = {The algebra $U_q(\hat{sl}_\infty)$ and applications},
  author = {David Hernandez},
  journal= {arXiv preprint arXiv:1001.3047},
  year   = {2011}
}

Comments

20 pages, 5 figures

R2 v1 2026-06-21T14:36:05.118Z