Abstract
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Our goal is to construct and study the multiplicity-free weight modules of quantum
affine algebras. For this, we introduce the notion of shiftability condition with respect
to a symmetrizable generalized Cartan matrix, and investigate its applications on
the study of quantum affine algebra structures and the realizations of the
infinite-dimensional multiplicity-free weight modules. We also compute the highest
-weights
of the infinite-dimensional multiplicity-free weight modules as highest
-weight
modules.
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Keywords
quantum affine algebra, representation theory,
multiplicity-free weight modules
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Mathematical Subject Classification
Primary: 17B10, 17B37
Secondary: 16T20, 20G42
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Milestones
Received: 27 February 2023
Revised: 15 December 2023
Accepted: 27 April 2024
Published: 13 September 2024
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Publishers). Distributed under the Creative Commons
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