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

In: Formal Power Series and Algebraic Combinatorics

Author

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  • Mercedes H. Rosas

    (Universidad Simón Bolívar, Departamento de Matemáticas)

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.

Suggested Citation

  • Mercedes H. Rosas, 2000. "The Kronecker Product of Schur Functions Indexed by Two-Row Shapes or Hook Shapes," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 344-355, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_31
    DOI: 10.1007/978-3-662-04166-6_31
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