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Search: MSC category 05E10 ( Combinatorial aspects of representation theory [See also 20C30] )

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1. CMB 2011 (vol 55 pp. 462)

Campbell, Peter S.; Stokke, Anna
 Hook-content Formulae for Symplectic and Orthogonal Tableaux 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 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. Keywords:symplectic tableaux, orthogonal tableaux, Schur functionCategories:05E05, 05E10

2. CMB 2010 (vol 53 pp. 453)

Desgroseilliers, Marc; Larose, Benoit; Malvenuto, Claudia; Vincent, Christelle
 Some Results on Two Conjectures of Schützenberger We present some partial results concerning two conjectures of SchÃ¼tzenberger on evacuations of Young tableaux. Keywords:Evacuation of Standard Young tableauxCategories:05E10, 05A99

3. CMB 2008 (vol 51 pp. 584)

Purbhoo, Kevin; Willigenburg, Stephanie van
 On Tensor Products of Polynomial Representations We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of $\GL(n,\mathbb{C})$ is isomorphic to another. As a consequence we discover families of Littlewood--Richardson coefficients that are non-zero, and a condition on Schur non-negativity. Keywords:polynomial representation, symmetric function, Littlewood--Richardson coefficient, Schur non-negativeCategories:05E05, 05E10, 20C30