辛同胚的一个Lefschetz不动点公式
A Lefschetz fixed point formula for symplectomorphisms
摘要：
考虑一个赋有预量子丛的紧致凯勒流形。按照几何量子化方案，相关的量子空间是前量子丛的张量幂幂的全纯截面的空间。本文构造了这些量子空间中的前量子丛自同构群的一个渐近表示。我们估计这些表示的一些横截性假设下的字符。所得公式在某种意义上推广了保全纯结构的前量子丛自同构的Lefschetz不动点公式。我们的结果将在两个即将举行的文件中应用到量子表示的映射类群。
英文摘要：
Consider a compact Kähler manifold endowed with a prequantum bundle. Following the geometric quantization scheme, the associated quantum spaces are the spaces of holomorphic sections of the tensor powers of the prequantum bundle. In this paper we construct an asymptotic representation of the prequantum bundle automorphism group in these quantum spaces. We estimate the characters of these representations under some transversality assumption. The formula obtained generalizes in some sense the Lefschetz fixed point formula for the automorphisms of the prequantum bundle preserving its holomorphic structure. Our results will be applied in two forthcoming papers to the quantum representation of the mapping class group.
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