Hook-content Formulae for Symplectic and Orthogonal Tableaux
Printed: Sep 2012
Peter S. Campbell
By considering the specialisation
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.
symplectic tableaux, orthogonal tableaux, Schur function
05E05 - Symmetric functions and generalizations
05E10 - Combinatorial aspects of representation theory [See also 20C30]