Flagged Littlewood-Richardson tableaux and branching rule for classical groups
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866916636594798592 |
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| author | Jang, Il-Seung Kwon, Jae-Hoon |
| author_facet | Jang, Il-Seung Kwon, Jae-Hoon |
| contents | 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 $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_11041 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Flagged Littlewood-Richardson tableaux and branching rule for classical groups Jang, Il-Seung Kwon, Jae-Hoon Representation Theory Combinatorics Quantum Algebra 17B37, 22E46, 05E10 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 $0$. |
| title | Flagged Littlewood-Richardson tableaux and branching rule for classical groups |
| topic | Representation Theory Combinatorics Quantum Algebra 17B37, 22E46, 05E10 |
| url | https://arxiv.org/abs/1908.11041 |