Geodesic
A Sundaram type bijection for \(\mathrm{SO}(3)\): vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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Motivated by the direct-sum-decomposition of the $r^{\text{th}}$ tensor power of the defining representation of the special orthogonal group $\mathrm{SO}(2k + 1)$, we present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for $\mathrm{SO}(3)$.Our bijection preserves a suitably defined descent set. Using it we determine the quasi-symmetric expansion of the Frobenius characters of the isotypic components.On the combinatorial side we obtain a bijection between Riordan paths and standard Young tableaux with 3 rows, all of even length or all of odd length.
DOI : 10.37236/7713
Classification : 05E10
Mots-clés : special orthogonal groups, vacillating tableaux, branching rules, Riordan paths

Judith Jagenteufel  1

1 TU Wien 
@article{10_37236_7713,
     author = {Judith Jagenteufel},
     title = {A {Sundaram} type bijection for {\(\mathrm{SO}(3)\):} vacillating tableaux and pairs of standard {Young} tableaux and orthogonal {Littlewood-Richardson} tableaux},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {3},
     doi = {10.37236/7713},
     zbl = {1396.05118},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7713/}
}
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Judith Jagenteufel. A Sundaram type bijection for \(\mathrm{SO}(3)\): vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7713

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