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Crystal structure on King tableaux and semistandard oscillating tableaux

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 نشر من قبل Seung Jin Lee
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English
 تأليف Seung Jin Lee




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In 1976, King defined certain tableaux model, called King tableaux in this paper, counting weight multiplicities of irreducible representation of the symplectic group $Sp(2m)$ for a given dominant weight. Since Kashiwara defined crystals, it is an open problem to provide a crystal structure on King tableaux. In this paper, we present crystal structures on King tableaux and semistandard oscillating tableaux. The semistandard oscillating tableaux naturally appear as $Q$-tableaux in the symplectic version of RSK algorithms. As an application, we discuss Littlewood-Richardson coefficients for $Sp(2m)$ in terms of semistandard oscillating tableaux.



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