On the Kronecker product of Schur functions of two row shapes
نویسندگان
چکیده
منابع مشابه
The Kronecker Product of Schur Functions Indexed by Two-Row Shapes or Hook Shapes
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 in χχ . We use Sergeev’s Formula for a S...
متن کاملOn the Kronecker Product of Schur Functions of Two Row Shapes
The Kronecker product of two homogeneous symmetric polynomials P1 and P2 is defined by means of the Frobenius map by the formula P1 ⊗ P2 = F (F−1P1)(F−1P2). When P1 and P2 are Schur functions sλ and sμ respectively, then the resulting product sλ ⊗ sμ is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the diagrams λ an...
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In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n large enough, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n when ...
متن کاملLecture 6 : Kronecker Product of Schur Functions – Part I
The irreducible representations of Sn, i.e. the Specht modules are indexed by partitions λ of n. For any two partitions λ, μ of n, Sλ ⊗ Sμ = gλμνSν , for suitable integers gλμν . The actual values of these coefficients still eludes us. We look at a formula (admittedly messy), which gives the exact values of gλμν for simple shapes λ, μ.
متن کاملRow-strict quasisymmetric Schur functions
Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the quasisymmetric Schur function basis, generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the row-strict quasisymmetric Schur...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 1994
ISSN: 1370-1444
DOI: 10.36045/bbms/1103408635