论文标题
szegökernels下的哈密顿$ su（2）\ times s^1 $ -Actions下的SzegöKernels
Equivariant asymptotics of Szegö kernels under Hamiltonian $SU(2)\times S^1$-actions
论文作者
论文摘要
令$ m $为复杂的投影歧管，$ a $ a a $ a正线捆绑包。假设一个紧凑型和连接的谎言组$ g $以$ m $的方式以hamiltonian和holomorphic的方式表现为$ m $，并且此操作将$ a $ a $ a $ a $。然后，在关联的代数数量耐用空间$ h（x）$上有一个相关的统一表示。 $ h（x）$上的标准圆圈动作以$ g $的操作，因此具有由$（k \，\boldsymbolν，\，k）$标记的分解，其中$ k \ in \ in \ mathbb {z} $和$ \ boldsymbol {n in \ in \ in \ in \ in \ hat \ hat \ hat \ hat \ hat \ g hat {g} $。我们将相应的均值投影仪的本地和全球渐近属性视为$ k $的无限。更笼统地，对于紧凑的连接谎言组，我们计算相应同种型的尺寸的渐近学。
Let $M$ be complex projective manifold and $A$ a positive line bundle on it. Assume that a compact and connected Lie group $G$ acts on $M$ in a Hamiltonian and holomorphic manner and that this action linearizes to $A$. Then, there is an associated unitary representation of $G$ on the associated algebro-geometric Hardy space $H(X)$. The standard circle action on $H(X)$ commutes with the action of $G$ and thus one has a decompositions labeled by $(k\,\boldsymbolν,\,k)$, where $k\in\mathbb{Z}$ and $\boldsymbol{ ν}\in \hat{G}$. We consider the local and global asymptotic properties of the corresponding equivariant projector as $k$ goes to infinity. More generally, for a compact connected Lie group, we compute the asymptotics of the dimensions of the corresponding isotypes.
