论文标题
通过线捆的共同体学代表理论
Representation Theory via Cohomology of Line Bundles
论文作者
论文摘要
令G为场k上的还原代数组，让B为G中的Borel子组。我们演示了Flag歧管G/B上线束的共同体的许多结果如何在G.的表示理论中产生了有趣的后果。我们的重点是K的特征是正面的。在这种情况下，对于g/b，线条束的共同体学模块的消失行为和非零共同体学模块的G结构仍然是很大的开放问题。我们对这些年来的发展进行了描述，试图说明现在已知的内容以及今天尚不清楚的事物。
Let G be a reductive algebraic group over a field k and let B be a Borel subgroup in G. We demonstrate how a number of results on the cohomology of line bundles on the flag manifold G/B have had interesting consequences in the representation theory for G. And vice versa. Our focus is on the case where the characteristic of k is positive. In this case both the vanishing behavior of the cohomology modules for a line bundle on G/B and the G-structures of the non-zero cohomology modules are still very much open problems. We give an account of the developments over the years, trying to illustrate what is now known and what is still not known today.
