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This article is cited in 55 scientific papers (total in 55 papers)
Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles
V. L. Popov
Abstract:
We construct models of finite-dimensional linear and projective irreducible representations of a connected semisimple group $G$ in linear systems on the variety $G$. We establish an algebro-geometric criterion for the linearizability of an irreducible projective representation of $G$. We explain the algebro-geometric meaning of the numerical characteristic of an arbitrary rational character of a maximal torus of $G$. Using these results we compute the Picard group of an arbitrary homogeneous space of any connected linear algebraic group $H$, prove the homogeneity of an arbitrary one-dimensional algebraic vector bundle over such a space relative to some covering group of $H$, and compute the Chern class of such a bundle.
Received: 18.04.1973
Citation:
V. L. Popov, “Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles”, Izv. Akad. Nauk SSSR Ser. Mat., 38:2 (1974), 294–322; Math. USSR-Izv., 8:2 (1974), 301–327
Linking options:
https://www.mathnet.ru/eng/im1903https://doi.org/10.1070/IM1974v008n02ABEH002107 https://www.mathnet.ru/eng/im/v38/i2/p294
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Abstract page: | 936 | Russian version PDF: | 334 | English version PDF: | 30 | References: | 57 | First page: | 4 |
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