发表机构
College of Science, Rikkyo University（立教大学理学部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对特殊正交李代数的两类组合模型，借助量子对称对的表示理论构造了二者间的自然双射，丰富了李代数表示理论的组合模型研究。
AI 中文摘要
正交型的Kashiwara–Nakashima表和Gelfand–Tsetlin模式是特殊正交李代数𝔰𝔬_N有限维不可约表示的著名组合模型，前者基于量子群的表示理论（尤其是晶体理论）构造，后者基于(𝔰𝔬_N,𝔰𝔬_{N-1})的分支规则构造。本文借助对应于(𝔰𝔬_N,𝔰𝔬_{N-1})的量子对称对的表示理论，在二者之间构造了一个自然的双射。
英文摘要
Kashiwara--Nakashima tableaux and Gelfand--Tsetlin patterns of orthogonal type are famous as combinatorial models of the finite-dimensional irreducible representations of the special orthogonal Lie algebras $\mathfrak{so}_N$. The former is constructed based on the representation theory of quantum groups, especially the theory of crystals, while the latter based on the branching rule for $(\mathfrak{so}_N,\mathfrak{so}_{N-1})$. In the present paper, we construct a natural bijection between them by means of the representation theory of quantum symmetric pairs corresponding to $(\mathfrak{so}_N,\mathfrak{so}_{N-1})$.
Comments52 pages
