The Kronecker Product of Schur Functions Indexed by Two-Row Shapes or Hook Shapes

Mercedes H. Rosas ()
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Mercedes H. Rosas: Universidad Simón Bolívar, Departamento de Matemáticas

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 344-355 from Springer

Abstract: Abstract The Kronecker product of two Schur functions s μ and s v , denoted by s μ * s v , is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions μ and v. The coefficient of s λ in this product is denoted by γ μv λ ,and corresponds to the multiplicity of the irreducible character X λ in X μ X v . We use Sergeev’s Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for s λ [XY] to find closed formulas for the Kronecker coefficients γ μv λ when λ is an arbitrary shape and μ and v are hook shapes or two-row shapes.

Keywords: Irreducible Representation; Symmetric Group; Symmetric Function; Kronecker Product; Irreducible Character (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04166-6_31

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DOI: 10.1007/978-3-662-04166-6_31

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