Invariant prime ideals in quantizations of nilpotent Lie algebras
Invariant prime ideals in quantizations of nilpotent Lie algebras
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幂零李代数量化中的不变素理想
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Yakimov
中科院分区：
文献类型：
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作者：
M. Yakimov
De Concini，Kac和Procesi定义了与相应的Weyl群W的元素相关的量子化泛包络代数Q(G)的子代数？W+，它们是泛包络代数？(n+∩adw(n−))的变形，其中n±是对偶Borel子代数的零根。基于Gorelik和Joseph的结果和对W+作为Schubert胞腔上函数的量子化代数的解释，我们明确地构造了每个W+的H不变素理想，并证明了相应的偏序集与W⩽w同构，其中H是q(G)的类群元素群.此外，对于W+的每个H-素数，我们用与基本表示有关的Demazure模构造了一个生成集。利用Ramanathan和Kempf的结果，我们证明了旗簇Schubert胞上相关Poisson结构的辛叶的环面轨道的闭理想为零的类似定理。
De Concini, Kac, and Procesi defined a family of subalgebras ?w+ of a quantized universal enveloping algebra ?q( g ), associated to the elements of the corresponding Weyl group W. They are deformations of the universal enveloping algebras ?( n+∩ Adw( n−)), where n± are the nilradicals of a pair of dual Borel subalgebras. Based on the results of Gorelik and Joseph and an interpretation of ?w+ as quantized algebras of functions on Schubert cells, we construct explicitly the H‐invariant prime ideals of each ?w+ and show that the corresponding poset is isomorphic to W⩽w, where H is the group of group‐like elements of ?q( g ). Moreover, for each H‐prime of ?w+ we construct a generating set in terms of Demazure modules related to fundamental representations. Using the results of Ramanathan and Kempf, we prove similar theorems for vanishing ideals of closures of torus orbits of symplectic leaves of related Poisson structures on Schubert cells in flag varieties.
量子格拉斯曼的素理想
DOI：
10.1007/s00029-008-0054-z
发表时间：
2008
期刊：
Selecta Mathematica
影响因子：
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作者：
Launois S
通讯作者：
Launois S