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ID 57813
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Author
Hiroshima, Toya Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University
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.
Keywords
Kashiwara crystals
Littlewood-Richardson crystals
Kashiwara-Nakashima tableaux
Branching rule
Note
Mathematics Subject Classification. Primary 05E10; Secondary 20G42.
Published Date
2020-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume62
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
87
End Page
178
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol62/iss1/3