PICARD GROUPS OF HOMOGENEOUS SPACES OF LINEAR ALGEBRAIC GROUPS AND ONE-DIMENSIONAL HOMOGENEOUS VECTOR BUNDLES
PICARD GROUPS OF HOMOGENEOUS SPACES OF LINEAR ALGEBRAIC GROUPS AND ONE-DIMENSIONAL HOMOGENEOUS VECTOR BUNDLES
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线性代数群齐次空间的PICARD群和一维齐次向量丛
DOI：
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发表时间：
1974
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通讯作者：
V. Popov
中科院分区：
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作者：
V. Popov
我们在簇 G 的线性系统中构建了连通半单群 G 的有限维线性和射影不可约表示模型。我们为 G 的不可约射影表示的线性化建立了代数几何准则。我们解释了 G 的最大环面的任意有理特征的数值特征的代数几何意义。利用这些结果，我们计算了任何连通线性代数群 H 的任意齐次空间的皮卡德群，证明了同质性相对于 H 的某个覆盖群，在这样的空间上建立任意一维代数向量丛，并计算这样的丛的 Chern 类。
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.