Asymptotics of standard modules of quantum affine algebras

2017/12/01 by Léa Bittmann, Bittmann, Léa
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1712.00355

32 pages, v2 : several technical Lemmas generalized and typos corrected

arxiv created 2018/04/22 · arxiv updated 2018/04/24

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 \mathfrakg=\mathfraksl₂, 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 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 O.

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