The Kronecker Product of Schur Functions Indexed by Two-Row Shapes or Hook Shapes
By Mercedes H. Rosas. 2000
101 citations recorded by the source corpus.
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 γλμν, and corresponds to the multiplicity of the irreducible character χλ in χμχν.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 γλμν when λ is an arbitrary shape and μ and ν are hook shapes or two-row shapes.Remmel (J.B. Remmel, J. Algebra120 (1989), 100–118; Discrete Math.99 (1992), 265–287) and Remmel and Whitehead (J.B. Remmel and T. Whitehead, Bull. Belg. Math. Soc. Simon Stiven1 (1994), 649–683) derived some closed formulas for the Kronecker product of Schur functions indexed by two-row shapes or hook shapes using a different approach. We believe that the approach of this paper is more natural. The formulas obtained are simpler and reflect the symmetry of the Kronecker product.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/da97afd5f3b8f6bd8c82d266cfcb30cee90afc5c
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In Discrete Mathematics and Combinatorics
- Arthur L. B. Yang
- Jonah Blasiak
- Larry X. W. Wang
- Cristina M. Ballantine
- William Y. C. Chen
- Rosa C. Orellana
In Geometry and Topology
- Arthur L. B. Yang
- Jonah Blasiak
- Larry X. W. Wang
- Cristina M. Ballantine
- William Y. C. Chen
- Rosa C. Orellana
Citations in the corpus
- Schur positivity and the q-log-convexity of the Narayana polynomials (2008, background): “Such Schur functions are of particular interest for their own sake; see, for example, Rosas [25], and Remmel and Whitehead [24].”
- A COMBINATORIAL INTERPRETATION FOR THE COEFFICIENTS IN THE KRONECKER PRODUCT s(n p;p) s (2005, background): “In recent years Lascoux [5], Remmel [7, 8], Remmel and Whitehead [9] and Rosas [11] derived closed formulas for Kronecker products of Schur functions indexed by two row shapes or hook shapes.”
- Hopf Algebras in Combinatorics (2014, unknown): “, [176]).”
- Kronecker coefficients for one hook shape (2012, background): “Remmel [26], and later Rosas [28], gave formulas for the case that λ is a two row shape and μ is a hook shape.”