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

Abstract

In this note we consider the algebra $U_q({\widehat{sl}}_{\infty })$ 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 $U_q({\widehat{sl}}_{\infty })$ viewed as representations of quantum toroidal algebras, that we prove for Kirillov-Reshetikhin modules.

20 pages, 5 figures

References in corpus (1)

• Quiver varieties and cluster algebras