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arXiv · 1810.02103

Quantum nilpotent subalgebras of classical quantum groups and affine crystals

Il-Seung Jang·Jae-Hoon Kwon
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Abstract

We study the crystal of quantum nilpotent subalgebra of $U_q(D_n)$ associated to a maximal Levi subalgebra of type $A_{n-1}$. We show that it has an affine crystal structure of type $D_n^{(1)}$ isomorphic to a limit of perfect Kirillov-Reshetikhin crystal $B^{n,s}$ for $s\geq 1$, and give a new polytope realization of $B^{n,s}$. We show that an analogue of RSK correspondence for type $D$ due to Burge is an isomorphism of affine crystals and give a generalization of Greene's formula for type $D$.

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BibTeXRIS

Il-Seung Jang, Jae-Hoon Kwon. 2018-10-04. Quantum nilpotent subalgebras of classical quantum groups and affine crystals. https://doi.org/10.1016/j.jcta.2019.06.004

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