论文标题
双旗品种和斯坦伯格地图的轨道嵌入
Orbit embedding for double flag varieties and Steinberg map
论文作者
论文摘要
在本文上半年，我们回顾了对称对的双旗品种的Steinberg理论。对于AIII类型的对称空间的特殊情况，我们将考虑$ x = gl_ {2n} / p _ {（n，n，n）} \ times gl_n / b_n / b_n^+ \ times gl_n / b_n^ - $ k = gl_n \ gl_n \ times gl_n \ times gl_n $ actips diagonally。我们在$ x $中对$ k $ - 孔进行分类，并对Steinberg Maps的明确组合描述进行分类。 在后半部分，我们将双标志品种嵌入到较大的标志中的理论。这种嵌入是一种强大的工具，可以根据已知品种研究不同类型的双标志品种。我们证明了轨道嵌入的轨道定理完全普遍，并给出了CI型的示例，该定理嵌入了AIII型中。
In the first half of this article, we review the Steinberg theory for double flag varieties for symmetric pairs. For a special case of the symmetric space of type AIII, we will consider $ X = GL_{2n}/P_{(n,n)} \times GL_n / B_n^+ \times GL_n / B_n^- $ on which $ K = GL_n \times GL_n $ acts diagonally. We give a classification of $ K $-orbits in $ X $, and explicit combinatorial description of the Steinberg maps. In the latter half, we develop the theory of embedding of a double flag variety into a larger one. This embedding is a powerful tool to study different types of double flag varieties in terms of the known ones. We prove an embedding theorem of orbits in full generality and give an example of type CI which is embedded into type AIII.
