| ID | 57813 |
| FullText URL | |
| Author |
Hiroshima, Toya
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University
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| Abstract | The branching coefficients of the tensor product of finite-dimensional irreducible Uq(g)-modules, where g is so(2n + 1, C) (Bn-type), sp(2n,C) (Cn-type), and so(2n,C) (Dn-type), are expressed in
terms of Littlewood-Richardson (LR) coefficients in the stable region. We give an interpretation of this relation by Kashiwara’s crystal theory by providing an explicit surjection from the LR crystal of type Cn to the disjoint union of Cartesian product of LR crystals of An−1-type and by proving that LR crystals of types Bn and Dn are identical to the corresponding LR crystal of type Cn in the stable region.
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| Keywords | Kashiwara crystals
Littlewood-Richardson crystals
Kashiwara-Nakashima tableaux
Branching rule
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| Note | Mathematics Subject Classification. Primary 05E10; Secondary 20G42.
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| Published Date | 2020-01
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| Publication Title |
Mathematical Journal of Okayama University
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| Volume | volume62
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| Issue | issue1
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| Publisher | Department of Mathematics, Faculty of Science, Okayama University
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| Start Page | 87
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| End Page | 178
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| ISSN | 0030-1566
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| NCID | AA00723502
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| Content Type |
Journal Article
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| language |
English
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| Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
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| File Version | publisher
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| Refereed |
True
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| Submission Path | mjou/vol62/iss1/3
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