Flagged Littlewood-Richardson tableaux and branching rule for classical groups
Il-Seung Jang, Jae-Hoon Kwon
备注：
50 pages, revised introduction, reference added, Corollary 4.12 added, comments added on Remark 3.22, 4.15, 4.19 and 5.8, comments added for Sections 3 and 6, to appear in Journal of Combinatorial Theory, Series A
发表信息：
Journal of Combinatorial Theory, Series A, 181, (2021), 105419
本文推广Littlewood限制公式，提出了从${\ m GL}_n$到${\ m O}_n$分支规则的新公式，该公式基于带标志条件的Littlewood-Richardson表，并据此给出了$B_n$和$D_n$型Lusztig $t$-权重重数的组合公式。
摘要：
我们给出了从${\ m GL}_n$到${\ m O}_n$的分支规则的新公式，推广了Littlewood限制公式。该公式以带有特定标志条件的Littlewood-Richardson表表示，这些条件在稳定范围内消失。作为应用，我们给出了具有最高权$μ$和权$0$的$B_n$和$D_n$型Lusztig $t$-权重重数$K_{μ0}(t)$的组合公式。
英文摘要：
We give a new formula for the branching rule from ${\rm GL}_n$ to ${\rm O}_n$ generalizing the Littlewood's restriction formula. The formula is given in terms of Littlewood-Richardson tableaux with certain flag conditions which vanish in a stable range. As an application, we give a combinatorial formula for the Lusztig $t$-weight multiplicity $K_{μ0}(t)$ of type $B_n$ and $D_n$ with highest weight $μ$ and weight $0$.
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