Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels

JOURNAL OF ALGEBRA

卷:374

Article

Naoi, Katsuyuki

关键词: Kirillov-Reshetikhin crystal;    Demazure crystal;    Energy function;   

DOI  :  10.1016/j.jalgebra.2012.10.020

来源: Elsevier

【 摘 要 】

In this paper, we study a tensor product of perfect Kirillov-Reshetikhin crystals (KR crystals for short) whose levels are not necessarily equal. We show that, by tensoring with a certain highest weight element, such a crystal becomes isomorphic as a full subgraph to a certain disjoint union of Demazure crystals contained in a tensor product of highest weight crystals. Moreover, we show that this isomorphism preserves their Z-gradings, where the Z-grading on the tensor product of KR crystals is given by the energy function, and that on the other side is given by the minus of the action of the degree operator. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free