sun123zxy's blog

sun123zxy's blog https://blog.sun123zxy.top/listings/draft/ Drafts WIP and shelved writings. https://blog.sun123zxy.top/cirno-academic-waste.jpg sun123zxy's blog https://blog.sun123zxy.top/listings/draft/ 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 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 On the Rank and the Span Rank of Modules sun123zxy https://blog.sun123zxy.top/posts/20251118-rank/ math algebra commalg https://blog.sun123zxy.top/posts/20251118-rank/ Tue, 18 Nov 2025 00:00:00 GMT A Table of Lie Groups and Lie Algebras sun123zxy https://blog.sun123zxy.top/posts/20251016-lie/ math algebra lie https://blog.sun123zxy.top/posts/20251016-lie/ Thu, 16 Oct 2025 00:00:00 GMT 非结合代数括号制造艺术 sun123zxy https://blog.sun123zxy.top/posts/20251007-bracket-assoc/ ，可以有以下五种不同的括号方式： $((ab)c)d \quad (a(bc))d \quad (ab)(cd) \quad a((bc)d) \quad a(b(cd))$ ]]> math algebra lie combinatorics https://blog.sun123zxy.top/posts/20251007-bracket-assoc/ Tue, 07 Oct 2025 00:00:00 GMT Artin–Rees–Krull 乱炖 sun123zxy https://blog.sun123zxy.top/posts/20250804-artin-rees-krull/ math algebra https://blog.sun123zxy.top/posts/20250804-artin-rees-krull/ Mon, 04 Aug 2025 00:00:00 GMT 从一般线性群 $\operatorname{GL}_n(\mathbb F_q)$ 的 Sylow $p$-子群谈起 sun123zxy https://blog.sun123zxy.top/posts/20250712-gl-sylow/ 为素数， $q = p^\alpha$ ．我们引入一点先进的 $q$ -analog 记号： $\begin{aligned}[] [n]_q &:= \frac{q^n - 1}{q - 1} = q^{n-1} + q^{n-2} + \cdots + q + 1 \\ [n]_q! &:= \prod_{i=1}^{n} [i]_q \end{aligned}$ ]]> math algebra lie https://blog.sun123zxy.top/posts/20250712-gl-sylow/ Sat, 12 Jul 2025 00:00:00 GMT 神奇流形在哪里 sun123zxy https://blog.sun123zxy.top/posts/20250602-manifold/ is an $\mathbb R \to \mathbb T^2 \subset \mathbb C^2$ immersion (Note that it’s injective!). The corresponding immersed $1$ -submanifold is a Lie subgroup that is dense in $\mathbb T^2$ (by Dirichlet’s approximation theorem), which confirms that it is not an embedded submanifold. For more information, see [1, Example 4.20]. ]]> math geometry https://blog.sun123zxy.top/posts/20250602-manifold/ Mon, 02 Jun 2025 00:00:00 GMT