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Equivariant asymptotics of Szegö kernels under Hamiltonian $SU(2)$-actions
Asian Journal of Mathematics ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/ajm.2020.v24.n3.a6
Andrea Galasso, Roberto Paoletti

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:

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。
更新日期:2020-01-01
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