Schur Algebras and Global Bases: New Proofs of Old Vanishing Theorems
Schur Algebras and Global Bases: New Proofs of Old Vanishing Theorems
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Schur 代数和全局基：旧消失定理的新证明
DOI：
10.1006/jabr.1997.7030
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发表时间：
1997
影响因子：
0.9
通讯作者：
D. Woodcock
中科院分区：
文献类型：
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作者：
D. Woodcock
- 是的Kempf消失定理在一个领域的类似物。他证明的核心是使用柏原的wx 22晶体碱基的i弦结构来分析Demazure模块。这种分析对我们的治疗至关重要。这个问题的一个重要方面是观察到，一个最高的权重类别是修补在一起，在一个非常令人满意的方式从一个相当特殊的有限维wx代数集合的模块类别。这些是斯科特的准遗传代数34;在约化wx组设置他们是唐金的广义舒尔代数8。在博雷尔子群的情况下，他们是博雷尔舒尔代数研究Woodwx公鸡36。传统上，这些代数的结构是自上而下推导出来的：通常使用几何中的消失定理证明所讨论的范畴是最高权范畴，然后使用最高权范畴形式主义推导出相关代数的结果。在这里，我们把事情反过来。使用全球基地，我们表明，我们的代数修补在一起很好地在自己之间，恢复结果的全类U-Int和U=-Int的限制参数。K K
Ž. tised analogue of Kempf’s vanishing theorem over a field. The heart of his proof involves using the i-string structure of Kashiwara’s crystal bases wx 22 to analyse the Demazure modules. This analysis is crucial to our treatment. An important aspect of this subject is the observation that a highest weight category is patched together in a very satisfactory manner from the module categories of a collection of rather special finite-dimensional wx algebras. These are Scott’s quasi-hereditary algebras 34; in the reductive wx group setting they are Donkin’s generalised Schur algebras 8. In the Borel subgroup case they are the Borel Schur algebras studied in Woodwx cock 36. Traditionally, the structure of these algebras is deduced from the top down: one proves, typically using vanishing theorems from geometry, that the category in question is a highest weight category, then deduces results about the associated algebras using the highest weight category formalism. Here we turn matters around. Using the global bases, we show that our algebras patch together nicely among themselves, recovering results on the full categories U-Int and U=-Int by limiting arguments. k k
DOI：
10.1007/978-1-4612-9839-7
发表时间：
1971
期刊：
--
影响因子：
--
作者：
S. Lane
通讯作者：
S. Lane