Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Naoi, Katsuyuki¹  Scrimshaw, Travis² 

[1] Tokyo Univ Agr & Technol, Inst Engn, 2-24-16 Naka Cho, Koganei, Tokyo 1848588, Japan

[2] Univ Queensland, Sch Math & Phys, St Lucia, Qld 4072, Australia

关键词: Affine quantum group;    Kirillov-Reshetikhin crystal;    Crystal pseudobase;   

DOI  :  10.1016/j.jpaa.2020.106593

来源: Elsevier

【 摘 要 】

We prove that, in types E-6,7,8,((1)) F-4((1)) and E-6((1)) every Kirillov-Reshetikhin module associated with the node adjacent to the adjoint one (near adjoint node) has a crystal pseudobase, by applying the criterion introduced by Kang et al. In order to apply the criterion, we need to prove some statements concerning values of a bilinear form. We achieve this by using the global bases of extremal weight modules. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free