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arXiv · 1001.3047

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

David Hernandez
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Abstract

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

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David Hernandez. 2010-04-06. The algebra $U_q(\hat{sl}_\infty)$ and applications. https://arxiv.org/abs/1001.3047

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