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

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

2010-01-18

arxiv.org/abs/1001.3047v2

De Concini's issue of J. Algebra 329 (2011), no. 1, 147--162

Mathematics

Quantum Algebra

20 pages, 5 figures

Scientific paper

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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