Hook-content Formulae for Symplectic and Orthogonal Tableaux

Canadian mathematical bulletin

Peter S. Campbell¹ 

[1] Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB R3B 2E9

关键词: symplectic tableaux;    orthogonal tableaux;    Schur function;   

DOI  :  10.4153/CMB-2011-105-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

By considering the specialisation$s_{lambda}(1,q,q^2,dots,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $lambda$ in terms ofthe 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 semistandardsymplectic and orthogonal $lambda$-tableaux.

【 授权许可】

Unknown