论文标题
覆盖$ \ Mathsf {iRREP}（s_n）$带有张量的产品和功率
Covering $\mathsf{Irrep}(S_n)$ With Tensor Products and Powers
论文作者
论文摘要
我们研究对称组$ s_n $的不可还原表示的张量产品包含所有不可减数作为子代理；我们说这样的张量产品覆盖$ \ mathsf {irrep}（s_n）$。我们的结果表明，这种行为是典型的。我们首先给出了张量产品的一般标准，以使其具有该特性，该特性几乎肯定地肯定地用于（Plancherel或均匀）随机不可减少的恒定尺寸集合。我们还考虑了覆盖$ \ mathsf {irrep}（s_n）$所需的单个固定不可减至的表示的最小张量功率。在这里，一个简单的下限来自考虑尺寸，我们表明它总是紧密地达到了普遍的常数因素，正如Liebeck，Shalev和Tiep最近提出的那样。
We study when a tensor product of irreducible representations of the symmetric group $S_n$ contains all irreducibles as subrepresentations; we say such a tensor product covers $\mathsf{Irrep}(S_n)$. Our results show that this behavior is typical. We first give a general sufficient criterion for tensor products to have this property, which holds asymptotically almost surely for constant-sized collections of (Plancherel or uniformly) random irreducibles. We also consider the minimal tensor power of a single fixed irreducible representation needed to cover $\mathsf{Irrep}(S_n)$. Here a simple lower bound comes from considering dimensions, and we show it is always tight up to a universal constant factor as was recently conjectured by Liebeck, Shalev, and Tiep.
