Algebras and Representation Theory

, Volume 22, Issue 5, pp 1209–1237 | Cite as

Asymptotics of Standard Modules of Quantum Affine Algebras

  • Léa BittmannEmail author


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 \(\mathfrak {g} = \hat {\mathfrak {s}\mathfrak {l}_{2}}\), 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 \(\mathcal {O}\).


Quantum affine algebra Category \(\mathcal {O}\) Standard modules 

Mathematics Subject Classification (2010)

16T20 17B10 17B37 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.CNRS Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586Université Paris-DiderotCedex 13France

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