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A Holomorphic Version of Borel–Weil–Bott Theorem

✍ Scribed by Simon G Gindikin; Hon-Wai Wong

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
436 KB
Volume
130
Category
Article
ISSN
0001-8708

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✦ Synopsis

A new geometric realization is obtained for finite dimensional representations of a complex reductive group. The representations are realized as holomorphic objects on a homogeneous Stein manifold. Fundamental to the construction is a holomorphic version of a Hodge decomposition. In certain important cases, the key underlying geometric structure in this decomposition is a certain kind of generalized conformal structure, which generalizes the twistor structures on Gr(2, 4).

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