ISSN:
0025-5874
Keywords:
Mathematics Subject Classification (1991): 22E46, 32M10.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let G be a complex connected semi-simple Lie group, with parabolic subgroup P. Let (P,P) be its commutator subgroup. The generalized Borel-Weil theorem on flag manifolds has an analogous result on the Dolbeault cohomology $H^{0,q}(G/(P,P))$ . Consequently, the dimension of $H^{0,q}(G/(P,P))$ is either 0 or $\infty$ . In this paper, we show that the Dolbeault operator $\bar\partial$ has closed image, and apply the Peter-Weyl theorem to show how q determines the value 0 or $\infty$ . For the case when P is maximal, we apply our result to compute the Dolbeault cohomology of certain examples, such as the punctured determinant bundle over the Grassmannian.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00004707
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