论文标题
SAXL猜想的张量立方体版本
A Tensor-Cube Version of the Saxl Conjecture
论文作者
论文摘要
令$ n $为正整数，让$ρ_n=（n，n-1，n-2，\ ldots，1）$为``楼梯''''''''''' SAXL的猜想断言，对称组的每个不可约表示$ s^λ$作为张量广场$ s^{ρ_n} \ otimes s^{ρ_n} $的子表示。在此简短说明中，我们表明，$ s_n $的每个不可减至表示形式出现在张量cube $ s^{ρ_n} \ otimes s^{ρ_n} \ otimes s^{ρ_n} $中。
Let $n$ be a positive integer, and let $ρ_n = (n, n-1, n-2, \ldots, 1)$ be the ``staircase'' partition of size $N = {n+1 \choose 2}$. The Saxl conjecture asserts that every irreducible representation $S^λ$ of the symmetric group $S_N$ appears as a subrepresentation of the tensor square $S^{ρ_n} \otimes S^{ρ_n}$. In this short note we show that every irreducible representation of $S_N$ appears in the tensor cube $S^{ρ_n} \otimes S^{ρ_n} \otimes S^{ρ_n}$.
