Holomorphic slices, symplectic reduction and multiplicities of representations
Holomorphic slices, symplectic reduction and multiplicities of representations
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全纯切片、辛约简和表示的多重性
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发表时间：
1993
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通讯作者：
Reyer Sjamaar
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作者：
Reyer Sjamaar
证明了K“Ahler流形上的约化复李群在某些轨道上作用的切片的存在性，即那些与群的紧实形式作用的动量映射的零水平集相交的轨道.给出了这一结果在动量映射的奇异水平上的辛约化和几何量子化中的应用.特别地，我得到了量子化中不可约表示的重数公式，其形式是约化空间的辛不变量，推广了Guillmin和Sternberg的一个结果.
I prove the existence of slices for an action of a reductive complex Lie group on a K"ahler manifold at certain orbits, namely those orbits that intersect the zero level set of a momentum map for the action of a compact real form of the group. I give applications of this result to symplectic reduction and geometric quantization at singular levels of the momentum map. In particular, I obtain a formula for the multiplicities of the irreducible representations occurring in the quantization in terms of symplectic invariants of reduced spaces, generalizing a result of Guillemin and Sternberg.