论文标题
Gelfand-Kirillov尺寸和最高重量模块的相关品种
Gelfand-Kirillov dimensions and associated varieties of highest weight modules
论文作者
论文摘要
在本文中，我们提出了lusztig的$ \ mathbf {a} $的统一公式 - 在经典的Weyl组上函数。然后，我们获得了一种有效的算法，该算法是经典谎言代数的简单最高权重模块的Gelfand-Kirillov尺寸，其最高权重不一定是规则或积分。为了处理$ d $ type $ d $，我们通过引入一个名为“空心塔塔”的不变式来证明有关Domino Tableaux的有趣物业。作为应用程序，明确确定了所有简单的最高权重harish-chandra模块的相关品种，包括特殊情况。
In this paper, we present a uniform formula of Lusztig's $ \mathbf{a}$-functions on classical Weyl groups. Then we obtain an efficient algorithm for the Gelfand-Kirillov dimensions of simple highest weight modules of classical Lie algebras, whose highest weight is not necessarily regular or integral. To deal with type $ D $, we prove an interesting property about domino tableaux by introducing an invariant, called the hollow tableau. As an application, the associated varieties of all the simple highest weight Harish-Chandra modules are explicitly determined, including the exceptional cases.
