A Sundaram type bijection for $\mathrm{SO}(2k+1)$: vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau
A Sundaram type bijection for $\mathrm{SO}(2k+1)$: vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau
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$mathrm{SO}(2k 1)$ 的 Sundaram 型双射：摇摆的画面和由标准 Young 画面和正交 Littlewood-Richardson 画面组成的对
DOI：
10.1090/s1088-4165-08-00329-4
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Judith Jagenteufel
中科院分区：
文献类型：
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作者：
Judith Jagenteufel
本文给出了特殊正交群$\mathrm{SO}（2k+1）$的摇摆表与由标准Young表和正交Littlewood-Richardson表组成的表对之间的双射。这个双射的动机是由$\mathrm{SO}（2k+1）$的定义表示的$r$次张量幂的直和分解。为了制定它，我们使用权的正交Littlewood-Richardson表，并引入新的替代表，他们在双射。此外，我们使用一个适当定义的下降集摇摆tableaux确定准对称扩展的Frobenius字符的同型组件。
We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group $\mathrm{SO}(2k+1)$. This bijection is motivated by the direct-sum-decomposition of the $r$th tensor power of the defining representation of $\mathrm{SO}(2k+1)$. To formulate it, we use Kwon's orthogonal Littlewood-Richardson tableaux and introduce new alternative tableaux they are in bijection with. Moreover we use a suitably defined descent set for vacillating tableaux to determine the quasi-symmetric expansion of the Frobenius characters of the isotypic components.