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- W1602806025 abstract "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." @default.
- W1602806025 created "2016-06-24" @default.
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- W1602806025 date "2000-02-19" @default.
- W1602806025 modified "2023-09-27" @default.
- W1602806025 title "Gerbes on complex reductive Lie groups" @default.
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