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June 2021 PBW theoretic approach to the module category of quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park
Proc. Japan Acad. Ser. A Math. Sci. 97(6): 33-37 (June 2021). DOI: 10.3792/pjaa.97.007

Abstract

Let $U_{q}'(\mathfrak{g})$ be a quantum affine algebra of untwisted affine ADE type and let $\mathcal{C}_{\mathfrak{g}}^{0}$ be Hernandez-Leclerc’s category. For a duality datum $\mathcal{D}$ in $\mathcal{C}_{\mathfrak{g}}^{0}$, we denote by $\mathcal{F}_{\mathcal{D}}$ the quantum affine Weyl-Schur duality functor. We give a sufficient condition for a duality datum $\mathcal{D}$ to provide the functor $\mathcal{F}_{\mathcal{D}}$ sending simple modules to simple modules. Moreover, under the same condition, the functor $\mathcal{F}_{\mathcal{D}}$ has compatibility with the new invariants introduced by the authors. Then we introduce the notion of cuspidal modules in $\mathcal{C}_{\mathfrak{g}}^{0}$, and show that all simple modules in $\mathcal{C}_{\mathfrak{g}}^{0}$ can be constructed as the heads of ordered tensor products of cuspidal modules. We next state that the ordered tensor products of cuspidal modules have the unitriangularity property.

Citation

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Masaki Kashiwara. Myungho Kim. Se-jin Oh. Euiyong Park. "PBW theoretic approach to the module category of quantum affine algebras." Proc. Japan Acad. Ser. A Math. Sci. 97 (6) 33 - 37, June 2021. https://doi.org/10.3792/pjaa.97.007

Information

Published: June 2021
First available in Project Euclid: 10 June 2021

Digital Object Identifier: 10.3792/pjaa.97.007

Subjects:
Primary: 17B37, 81R50
Secondary: 18D10

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 6 • June 2021
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