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arXiv · 1908.11041

Flagged Littlewood-Richardson tableaux and branching rule for classical groups

Il-Seung Jang·Jae-Hoon Kwon
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Abstract

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 $K_{\mu 0}(t)$ of type $B_n$ and $D_n$ with highest weight $\mu$ and weight $0$.

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BibTeXRIS

Il-Seung Jang, Jae-Hoon Kwon. 2019-08-29. Flagged Littlewood-Richardson tableaux and branching rule for classical groups. https://doi.org/10.1016/j.jcta.2021.105419

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