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摘要翻译：
有限维复约化李代数g的幂零双酮是g×g中元素的子集，其由分量生成的子空间包含在g的幂零锥中。这个注记的主要结果是幂零双酮是完全交。这肯定地回答了关于零锥的Kraft-Wallach猜想。此外，我们引入并研究了G的特征子模。幂零双酮和特征子模的性质对于理解交换簇及其定义的理想是非常重要的。为了研究幂零双锥，我们引入了另一个子变体--主双锥。幂零双锥，以及主双锥，都与喷气方案有关。我们利用母题积分中的参数来研究它们的维数。也就是说，我们遵循http://arxiv.org/abs/math/0008002v5中开发的方法。
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英文标题：
《Nilpotent bicone and characteristic submodule of a reductive Lie algebra》
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作者：
Jean-Yves Charbonnel (IMJ), Anne Moreau (LMA-Poitiers)
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最新提交年份：
2014
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分类信息：
一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The nilpotent bicone of a finite dimensional complex reductive Lie algebra g is the subset of elements in g x g whose subspace generated by the components is contained in the nilpotent cone of g. The main result of this note is that the nilpotent bicone is a complete intersection. This affirmatively answers a conjecture of Kraft-Wallach concerning the nullcone. In addition, we introduce and study the characteristic submodule of g. The properties of the nilpotent bicone and the characteristic submodule are known to be very important for the understanding of the commuting variety and its ideal of definition. In order to study the nilpotent bicone, we introduce another subvariety, the principal bicone. The nilpotent bicone, as well as the principal bicone, are linked to jet schemes. We study their dimensions using arguments from motivic integration. Namely, we follow methods developed in http://arxiv.org/abs/math/0008002v5 .
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PDF链接：
https://arxiv.org/pdf/0705.2685
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