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arXiv · 1902.03843

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

Judith Jagenteufel
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Abstract

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.

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Judith Jagenteufel. 2019-02-11. 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. https://arxiv.org/abs/1902.03843

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