Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that $SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to $A$. Then there is an associated unitary representation of $G$ on the associated algebro-geometric Hardy space, and the isotypical components are all finite dimensional. We consider the local and global asymptotic properties the equivariant projector associated to a weight $k \, \boldsymbol{ \nu }$, when $\boldsymbol{ \nu }$ is fixed and $k\rightarrow +\infty$.

中文翻译：

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哈密​​顿量$SU(2)$-actions下Szegö核的等变渐近

令 $M$ 为复射影流形，$A$ 为正线丛。假设 $SU(2)$ 以哈密顿方式作用于 $M$，矩图无处消失，并且该动作线性化为 $A$。然后在相关的代数几何哈代空间上有一个相关的 $G$ 的幺正表示，并且同型分量都是有限维的。当 $\boldsymbol{ \nu }$ 固定且 $k\rightarrow +\infty$ 时，我们考虑与权重 $k \, \boldsymbol{ \nu }$ 相关联的局部和全局渐近属性。