论文标题
拓扑Frobenius互惠和不变的Hermitian形式
Topological Frobenius reciprocity and invariant Hermitian forms
论文作者
论文摘要
戴维·沃根（David Vogan）在他的文章“统一表示和复杂分析”中给出了在某些均匀的分析式或骨上定义的连续不变的冬粒形式的表征，该形式是在广义国旗歧管中定义的某些均质分析式或骨。在手稿的最后一部分中，沃根（Vogan）提出了一个问题，即这些表示形式的拓扑结构互惠的可能性。在本文中，我们在常规的，抗利用的情况下给出了拓扑互惠的特定版本，并使用它来研究连续不变的Hermitian形式在造成的共同体上的存在。特别是，我们在几何纤维上的捆层共同体学上获得了自然关系和不变的形式。
In his article "Unitary Representations and Complex Analysis", David Vogan gives a characterization of the continuous invariant Hermitian forms defined on the compactly supported sheaf cohomology groups of certain homogeneous analytic sheaves defined on open orbits in generalized flag manifolds. In the last section of the manuscript, Vogan raises a question about the possibility of a topological Frobenius reciprocity for these representations. In this article we give a specific version of the topological reciprocity in the regular, antidominant case and use it to study the existence of continuous invariant hermitian forms on the sheaf cohomology. In particular, we obtain a natural relationship between invariant forms on the sheaf cohomology and invariant forms on the geometric fiber.
