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arXiv · 1712.00355

Asymptotics of standard modules of quantum affine algebras

Léa Bittmann
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Abstract

We introduce a sequence of $q$-characters of standard modules of a quantum affine algebra and we prove it has a limit as a formal power series. For $\mathfrak{g}=\hat{\mathfrak{sl}_{2}}$, we establish an explicit formula for the limit which enables us to construct corresponding asymptotical standard modules associated to each simple module in the category $\mathcal{O}$ of a Borel subalgebra of the quantum affine algebra. Finally, we prove a decomposition formula for the limit formula into $q$-characters of simple modules in this category $\mathcal{O}$.

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Léa Bittmann. 2017-12-01. Asymptotics of standard modules of quantum affine algebras. https://arxiv.org/abs/1712.00355

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