Mathematical Journal of Okayama University 62巻 1号
2020-01 発行

Crystal interpretation of a formula on the branching rule of types Bn, Cn, and Dn

Hiroshima, Toya Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University
Publication Date
2020-01
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
Comments
Mathematics Subject Classification. Primary 05E10; Secondary 20G42.