Grassmannian扭曲、导出等价和膜输运
Grassmannian twists, derived equivalences and brane transport
摘要：
本文基于在波恩举行的String-Math 2012上的演讲，与Ed Segal的联合论文。我们表现出相应的格拉斯曼触发器导出的等价。这些等价性的构造受到Herbst-Hori-Page关于规范线性sigma模型的膜运输的工作的启发：特别是，我们定义了对应于其等级限制规则的“窗口”。然后，我们将展示如何组成我们的等价产生有趣的自等价，我们描述为扭曲和cotiwits某些球形函子。我们的证明使用自然长的确切序列的丛格拉斯曼称为扭曲的Lascoux复合体，或楼梯复合体。我们给这些紧凑的描述。我们还涉及一些相关的发展，并通过一些扩展的例子。
英文摘要：
This note is based on a talk given at String-Math 2012 in Bonn, on a joint paper with Ed Segal. We exhibit derived equivalences corresponding to certain Grassmannian flops. The construction of these equivalences is inspired by work of Herbst-Hori-Page on brane transport for gauged linear sigma models: in particular, we define 'windows' corresponding to their grade restriction rules. We then show how composing our equivalences produces interesting autoequivalences, which we describe as twists and cotwists about certain spherical functors. Our proofs use natural long exact sequences of bundles on Grassmannians known as twisted Lascoux complexes, or staircase complexes. We give a compact description of these. We also touch on some related developments, and work through some extended examples.
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