Quantum nilpotent subalgebras of classical quantum groups and affine crystals
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866917071658418176 |
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| author | Jang, Il-Seung Kwon, Jae-Hoon |
| author_facet | Jang, Il-Seung Kwon, Jae-Hoon |
| contents | 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 $D$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_02103 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Quantum nilpotent subalgebras of classical quantum groups and affine crystals Jang, Il-Seung Kwon, Jae-Hoon Quantum Algebra Combinatorics 17B37, 22E46, 05E10 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 $D$. |
| title | Quantum nilpotent subalgebras of classical quantum groups and affine crystals |
| topic | Quantum Algebra Combinatorics 17B37, 22E46, 05E10 |
| url | https://arxiv.org/abs/1810.02103 |