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The Kronecker product of Schur functions indexed by two-row shapes or hook shapes

Opened Access The Kronecker product of Schur functions indexed by two-row shapes or hook shapes

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Autor: Rosas Celis, Mercedes Helena
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2001-09
Publicado en: Journal of algebraic combinatorics, 14 (2), 153-173.
Tipo de documento: Artículo
Resumen: The Kronecker product of two Schur functions sµ and sν, denoted by sµ ∗ sν, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions µ and ν. The coefficient of sλ in this product is denoted by γ λ µν , and corresponds to the multiplicity of the irreducible character χ λ in χ µχ ν We use Sergeev’s Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for sλ[XY ] to find closed formulas for the Kronecker coefficients γ λ µν when λ is an arbitrary shape and µ and ν are hook shapes or two-row shapes. Remmel [9 J.B. Remmel, “A formula for the Kronecker product of Schur functions of hook shapes,” J. Algebra 120, 1989, pp. 100–118, 10 J.B. Remmel, “Formulas for the expansion of the Kronecker products S(m,n) ⊗ S(1p−r,r) and S(1k2 l) ⊗ S(1p−r,r) ,” Discrete Math. 99, 1992, pp. 265–287] and Remmel and Whitehead [11] J.B. Remmel and T. Whitehead, “On the Kroneck...
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Cita: Rosas Celis, M.H. (2001). The Kronecker product of Schur functions indexed by two-row shapes or hook shapes. Journal of algebraic combinatorics, 14 (2), 153-173.
Tamaño: 241.4Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41689

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

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