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 \(\mathfrak {g} = \hat {\mathfrak {s}\mathfrak {l}_{2}}\), 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 \(\mathcal {O}\).
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Presented by: Vyjayanthi Chari
The author is supported by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement number 647353 Qaffine.
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Bittmann, L. Asymptotics of Standard Modules of Quantum Affine Algebras. Algebr Represent Theor 22, 1209–1237 (2019). https://doi.org/10.1007/s10468-018-9818-0
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DOI: https://doi.org/10.1007/s10468-018-9818-0