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arXiv · 1903.11681

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

Katsuyuki Naoi·Travis Scrimshaw
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Abstract

We prove that, in types $E_{6,7,8}^{(1)}$, $F_4^{(1)}$ and $E_6^{(2)}$, 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.

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Katsuyuki Naoi, Travis Scrimshaw. 2019-03-27. Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types. https://doi.org/10.1016/j.jpaa.2020.106593

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