The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
| dc.creator | Rosas, Mercedes H. | |
| dc.date | 2000-01-14 | |
| dc.date.accessioned | 2026-07-07T04:33:20Z | |
| dc.date.available | 2026-07-07T04:33:20Z | |
| dc.description | The Kronecker product of two Schur functions $s_μ$ and $s_ν$, denoted by $s_μ*s_ν$, 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 $s_λ$ 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 $s_λ[XY]$ 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 \cite{Re1, Re2} and Remmel and Whitehead \cite{Re-Wh} 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. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0001084 | |
| dc.identifier | http://arxiv.org/abs/math/0001084 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58534 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 05E10; 05E05 | |
| dc.title | The Kronecker product of Schur functions indexed by two-row shapes or hook shapes | |
| dc.type | text |