English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a bijection between vacillating tableaux and pairs consisting of astandard Young tableau and an orthogonal Littlewood-Richardson tableau for thespecial orthogonal group $\mathrm{SO}(2k+1)$. This bijection is motivated bythe direct-sum-decomposition of the $r$th tensor power of the definingrepresentation of $\mathrm{SO}(2k+1)$. To formulate it, we use Kwon'sorthogonal Littlewood-Richardson tableaux and introduce new alternativetableaux they are in bijection with. Moreover we use a suitably defined descentset for vacillating tableaux to determine the quasi-symmetric expansion of theFrobenius characters of the isotypic components.

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