Geodesic
The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
Journal of Algebraic Combinatorics, Tome 14 (2001) no. 2, pp. 153-173.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The Kronecker product of two Schur functions $s \_$ mgr and s _ ngr, denoted by s _ mgr$ * s \_$ ngr, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions $mgr$ and $ngr$. The coefficient of $s \_$ lambda in this product is denoted by $gamma ^$ lambda_ mgrngr, and corresponds to the multiplicity of the irreducible character $chi ^$ lambda in $chi^{ $mgr$}chi ^$ ngr. We use Sergeev"s Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for $s \_{ $lambda$}[ XY]$ to find closed formulas for the Kronecker coefficients $gamma ^$ lambda_ mgrngr when $lambda$ is an arbitrary shape and $mgr$ and $ngr$ are hook shapes or two-row shapes.
Keywords: Kronecker product internal product, sergeev"s formula 
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     author = {Rosas, Mercedes H.},
     title = {The {Kronecker} product of {Schur} functions indexed by two-row shapes or hook shapes},
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Rosas, Mercedes H. The Kronecker product of Schur functions indexed by two-row shapes or hook shapes. Journal of Algebraic Combinatorics, Tome 14 (2001) no. 2, pp. 153-173. http://geodesic.mathdoc.fr/item/JAC_2001__14_2_a0/