论文标题
旗歧管上的显式伪卡勒指标
Explicit Pseudo-Kähler Metrics on Flag Manifolds
论文作者
论文摘要
紧凑型谎言组的共同连接轨道各有一个规范（积极的）kähler结构，以著名的方式实现该小组在适当的线捆绑包（Borel-Weil定理）的全体形态段中的不可减至表示。研究较少的是（不确定的）不变 *伪 *-kähler结构，它们也可以用来实现各节（Bott的定理）中较高共同体中相同的表示。使用``eigenflag''嵌入，在统一组的情况下，我们对这些指标进行了非常明确的描述。作为副产品，我们表明$ u_n/（u_ {n_1} \ times \ cdots \ times \ times u_ {n_k}）$具有$ k！$不变的复杂结构，这一数量似乎迄今已引起了注意。
The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) Kähler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil theorem). Less studied are the (indefinite) invariant *pseudo*-Kähler structures they also admit, which can be used to realize the same representations in higher cohomology of the sections (Bott's theorem). Using ``eigenflag'' embeddings, we give a very explicit description of these metrics in the case of the unitary group. As a byproduct we show that $U_n/(U_{n_1}\times\cdots\times U_{n_k})$ has exactly $k!$ invariant complex structures, a count which seems to have hitherto escaped attention.
