Abstract
The aim of this paper is to study the graded limits of minimal affinizations over the quantum loop algebra of type G 2. We show that the graded limits are isomorphic to multiple generalizations of Demazure modules, and obtain defining relations of them. As an application, we obtain a polyhedral multiplicity formula for the decomposition of minimal affinizations of type G 2 as a \(U_{q}(\mathfrak {g})\)-module, by showing the corresponding formula for the graded limits. As another application, we prove a character formula of the least affinizations of generic parabolic Verma modules of type G 2 conjectured by Mukhin and Young.
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Presented by Vyjayanthi Chari.
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Li, JR., Naoi, K. Graded Limits of Minimal Affinizations over the Quantum Loop Algebra of Type G 2 . Algebr Represent Theor 19, 957–973 (2016). https://doi.org/10.1007/s10468-016-9606-7
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DOI: https://doi.org/10.1007/s10468-016-9606-7