...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Mathematical Proceedings of the Cambridge Philosophical Society >Projections of the minimal nilpotent orbit in a simple Lie algebra and secant varieties
【24h】

Projections of the minimal nilpotent orbit in a simple Lie algebra and secant varieties

机译：

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Let G be a simple algebraic group with g = Lie G and Omin C g the minimal nilpotent orbit. For a Z2-grading g = g0 (R) g1, let G0 be a connected subgroup of G with Lie G0 = g0. We study the G0-equivariant projections ? : O(min )g0 and ?:O-min g1. It is shown that the properties of ?(O-min ) and ? (O-min ) essentially depend on whether the intersection O(min )n g1 is empty or not. If O-min n g1 =? 0, then both ?(O-min ) and ?(O-min ) contain a 1-parameter family of closed G0-orbits, while if O-min n g1 = 0, then both are G0-prehomogeneous. We prove that G.?(O-min ) = G.? (Omin). Moreover, if O-min n g1 =? 0, then this common variety is the affine cone over the secant variety of P(O-min ) C P(g). As a digression, we obtain some invariant-theoretic results on the affine cone over the secant variety of the minimal orbit in an arbitrary simple G-module. In conclusion, we discuss more general projections that are related to either arbitrary reductive subalgebras of g in place of g0 or spherical nilpotent G-orbits in place of Omin.

著录项

相似文献

  • 外文文献
  • 中文文献
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号