Geodesic
Hook-content Formulae for Symplectic and Orthogonal Tableaux
Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 462-473

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DOI

By considering the specialisation ${{s}_{\lambda }}(1,\,q,\,{{q}^{2}},\ldots ,\,{{q}^{n-1}})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $\lambda $ in terms of the contents and hook lengths of the boxes in the Young diagram. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal $\lambda $ -tableaux.
DOI : 10.4153/CMB-2011-105-7
Mots-clés : 05E05, 05E10, symplectic tableaux, orthogonal tableaux, Schur function 
Campbell, Peter S.; Stokke, Anna. Hook-content Formulae for Symplectic and Orthogonal Tableaux. Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 462-473. doi: 10.4153/CMB-2011-105-7
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     author = {Campbell, Peter S. and Stokke, Anna},
     title = {Hook-content {Formulae} for {Symplectic} and {Orthogonal} {Tableaux}},
     journal = {Canadian mathematical bulletin},
     pages = {462--473},
     year = {2012},
     volume = {55},
     number = {3},
     doi = {10.4153/CMB-2011-105-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-105-7/}
}
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