sun123zxy's blog

sun123zxy's blog https://blog.sun123zxy.top/listings/nilpcone/ The geometry of the nilpotent cone of $\mathfrak{gl}_n$. https://blog.sun123zxy.top/marisa-hat.jpg sun123zxy's blog https://blog.sun123zxy.top/listings/nilpcone/ quarto-1.9.34 Fri, 10 Apr 2026 00:00:00 GMT Lustig–Spaltenstein：分块幂零轨道的提升 sun123zxy https://blog.sun123zxy.top/posts/20260409-ncone-induced-orbit/ 中的 Lustig–Spaltenstein 提升：使用分块对角幂零轨道拼出整个 $\mathfrak{gl}_n$ 中的幂零轨道． ]]> math algebra lie https://blog.sun123zxy.top/posts/20260409-ncone-induced-orbit/ Fri, 10 Apr 2026 00:00:00 GMT Jacobson–Morozov：$\mathfrak{sl}_2$ 在复半单李代数中的嵌入 sun123zxy https://blog.sun123zxy.top/posts/20260410-jacobson-morozov/ 中工作，并假设抽象 Jordan 分解、Killing 型和 Cartan 根空间分解理论已建立完毕．这一部分的标准参考是 [1, section 3.2–3.3]． ]]> math algebra lie https://blog.sun123zxy.top/posts/20260410-jacobson-morozov/ Fri, 10 Apr 2026 00:00:00 GMT 幂零轨道的维数 sun123zxy https://blog.sun123zxy.top/posts/20260322-ncone-dim/ 上篇介绍了幂零锥和幂零轨道的基本概念．本篇我们关心 $\mathfrak{gl}_n$ 幂零锥和幂零轨道的维数情况． ]]> math algebra lie https://blog.sun123zxy.top/posts/20260322-ncone-dim/ Fri, 03 Apr 2026 00:00:00 GMT 作用群的选择 sun123zxy https://blog.sun123zxy.top/posts/20260330-ncone-ad-group/ 上篇中简单介绍了复数域上 $\mathfrak{gl}_n$ 或 $\mathfrak{sl}_n$ 的共轭 / 幂零轨道的定义．这是 ad hoc 的．一般来说，不同的群作用在李代数 $\mathfrak{g}$ 上可能导致不同的轨道．本篇介绍我们选择作用群的标准，主要参考 [1, section 1.2]． ]]> math algebra lie https://blog.sun123zxy.top/posts/20260330-ncone-ad-group/ Mon, 30 Mar 2026 00:00:00 GMT $\mathfrak{gl}_n$，幂零轨道与支配序 sun123zxy https://blog.sun123zxy.top/posts/20260321-geo-nilp-gln/ 或 $\mathfrak{sl}_n$ 切入，入门友好地为李代数上幂零锥的几何提供一些感觉． ]]> math algebra lie https://blog.sun123zxy.top/posts/20260321-geo-nilp-gln/ Sat, 21 Mar 2026 00:00:00 GMT