每日定理17
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(2.10) If $g\in G$ and $g\neq1$, then $\rho(g)=0.$ Also $\rho(1)=|G|$. Pf: Obviously. Isaac 阅读全文
posted @ 2019-05-08 16:23 群论之禅 阅读(116) 评论(0) 推荐(0)
每日定理16
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.9) Let $\mathfrak{X}$ and $\mathfrak{Y}$ be $\mathbb{C}$-representations of a group. 阅读全文
posted @ 2019-05-07 16:46 群论之禅 阅读(97) 评论(0) 推荐(0)
每日定理15
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(2.8) Every class function $\varphi$ of $G$ can be uniquely expressed in the form $$\varp 阅读全文
posted @ 2019-05-06 10:46 群论之禅 阅读(127) 评论(0) 推荐(0)
每日定理14
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.6) The group $G$ is abelian iff every irreducible character is linear. Pf: The numbe 阅读全文
posted @ 2019-05-04 16:24 群论之禅 阅读(149) 评论(0) 推荐(0)
每日定理13
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.5) The number $k$ of similarity classes of irreducible representations of $G$ is equ 阅读全文
posted @ 2019-05-03 09:39 群论之禅 阅读(112) 评论(0) 推荐(0)
每日定理12
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(2.4) Let $\mathcal{K}_1,~\mathcal{K}_2,\cdots,~\mathcal{K}_r$ be the conjugacy classes o 阅读全文
posted @ 2019-05-02 21:53 群论之禅 阅读(133) 评论(0) 推荐(0)
每日定理11
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(2.3) Pf: $tr(P^{-1}AP)=tr(A)$ $\mathfrak{X}(h^{-1}gh)=\mathfrak{X}(h)^{-1}\mathfrak{X}(g)\ 阅读全文
posted @ 2019-04-29 08:34 群论之禅 阅读(89) 评论(0) 推荐(0)
每日定理10
摘要：
Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(1.17) Let $A$ be a semisimple algebra over an algebraically closed field $F$ and let $ 阅读全文
posted @ 2019-04-28 18:51 群论之禅 阅读(115) 评论(0) 推荐(0)
浙公网安备 33010602011771号