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Graded Limits of Minimal Affinizations over the Quantum Loop Algebra of Type G 2

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Jian-Rong Li

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 9190401, Israel

    Jian-Rong Li

  3. Institute of Engineering, Tokyo University of Agriculture and Technology, 3-8-1 Harumi-cho, Fuchu-shi, Tokyo, Japan

    Katsuyuki Naoi

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  1. Jian-Rong Li
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  2. Katsuyuki Naoi
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Correspondence to Jian-Rong Li.

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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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