Gerbes on complex reductive Lie groups
Gerbes on complex reductive Lie groups
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Gerbes 论复数还原李群
DOI：
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发表时间：
2000
期刊：
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通讯作者：
J. Brylinski
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文献类型：
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作者：
J. Brylinski
本文在复约化李群G上构造了一个格，它依附于一个极大可对角化子代数上的不变双线性型，该极大可对角化子代数是Weyl群不变的，并且满足一个奇偶条件。通过对极大紧子群K的限制，得到了K上的一个格贝。对于单连通群，奇偶性条件与Pressley和Segal使用的相同;一般来说，它是由Deligne和作者引入的。gerbe是通过几何方法定义的，使用所谓的Grothendieck流形。它在G的共轭作用下是等变的;它对半单轨道的限制并不总是平凡的。本文首先讨论了格贝数据（在查特吉和希钦的意义上）和格贝几何对象（群胚层）;这两种方法之间的关系。有一个附录的equivariant gerbes，讨论从这两个观点。
We construct a gerbe over a complex reductive Lie group G attached to an invariant bilinear form on a maximal diagonalizable subalgebra which is Weyl group invariant and satisfies a parity condition. By restriction to a maximal compact subgroup K, one then gets a gerbe over K. For a simply-connected group, the parity condition is the same used by Pressley and Segal; in general, it was introduced by Deligne and the author. The gerbe is defined by geometric methods, using the so-called Grothendieck manifold. It is equivariant under the conjugation action of G; its restriction to a semisimple orbit is not always trivial. The paper starts with a discussion of gerbe data (in the sense of Chatterjee and Hitchin) and of gerbes as geometric objects (sheaves of groupoids); the relation between the two approaches is presented. There is an Appendix on equivariant gerbes, discussed from both points of view.
物理学家的拓扑、范畴论和微分几何
DOI：
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发表时间：
2006
期刊：
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作者：
S.;Tanimura
通讯作者：
Tanimura