论文标题
$ \ mathsf {su}（n）$的表示形式的渐近和催化遏制
Asymptotic and catalytic containment of representations of $\mathsf{SU}(n)$
论文作者
论文摘要
给定两个有限维表示$ρ$和$ \ $ \ mathsf {su}（n）$的$σ$，何时在\ mathbb {n} $中$ n \ n \ n \ n \ n} $，以至于$ρ^{\ otimes n} $是对$ $ f $σ^^{\ otimes n}的subsemorphic in Ismorphic osmorphic？什么时候有第三个表示$η$，以至于$ρ\ otimesη$是$σ\ otimesη$的子代表？我们将这些分别称为渐近和催化遏制的问题。 我们根据明确的不平等家庭回答两个问题。这些不平等在以下意义上几乎是必要的和足够的。如果两种表示严格满足了所有不平等，则随后渐近和催化遏制（在泛型情况下）。相反，如果渐近或催化遏制固定，则不等式必须非刻板性。这些结果是应用于表示半度的最新\ emph {vergleichsstellensatz}的实例。
Given two finite-dimensional representations $ρ$ and $σ$ of $\mathsf{SU}(n)$, when is there $n \in \mathbb{N}$ such that $ρ^{\otimes n}$ is isomorphic to a subrepresentation of $σ^{\otimes n}$? When is there a third representation $η$ such that $ρ\otimes η$ is a subrepresentation of $σ\otimes η$? We call these the questions of asymptotic and catalytic containment, respectively. We answer both questions in terms of an explicit family of inequalities. These inequalities are almost necessary and sufficient in the following sense. If two representations satisfy all inequalities strictly, then asymptotic and catalytic containment follow (the former in generic cases). Conversely, if asymptotic or catalytic containment holds, then the inequalities must hold non-strictly. These results are an instance of a recent \emph{Vergleichsstellensatz} applied to the representation semiring.
