The algebra [formula omitted] and applications

Abstract

In this note we consider the algebra U q ( sl ˆ ∞ ) and we study the category O of its integrable representations. The main motivations are applications to quantum toroidal algebras U q ( sl n + 1 tor ) , more precisely predictions of character formulae for representations of U q ( sl n + 1 tor ) . In this context, we state a general positivity conjecture for representations of U q ( sl ˆ ∞ ) viewed as representations of U q ( sl n + 1 tor ) , that we prove for Kirillov–Reshetikhin modules.