论文标题
关于实际还原组的分支定律的直接积分分解
On the direct integral decomposition in branching laws for real reductive groups
论文作者
论文摘要
真正还原的组$ g $的不可约合单一表示$π$ $ g $ $ g $ $ h $ $ h $分解为不可约合的单一表示的直接积分，$ h $ $ h $ a $ m（π，τ）\ in \ mathbb {n} n}我们表明，在$π$的平滑矢量上，直接积分是指定的。这意味着$ m（π，τ）$在上面的尺寸上，$ \ operatatorName {hom} _h（π^\ infty | _H，τ^\ indty）$在平稳矢量之间交织的操作员的互联媒体$，也称为对称性违反操作员，并提供了这些精确的相关性。
The restriction of an irreducible unitary representation $π$ of a real reductive group $G$ to a reductive subgroup $H$ decomposes into a direct integral of irreducible unitary representations $τ$ of $H$ with multiplicities $m(π,τ)\in\mathbb{N}\cup\{\infty\}$. We show that on the smooth vectors of $π$, the direct integral is pointwise defined. This implies that $m(π,τ)$ is bounded above by the dimension of the space $\operatorname{Hom}_H(π^\infty|_H,τ^\infty)$ of intertwining operators between the smooth vectors, also called symmetry breaking operators, and provides a precise relation between these two concepts of multiplicity.
