: 鐃緒申鐃緒申文鐃緒申砲弔鐃緒申鐃�...

鐃緒申鐃緒申鐃�II鐃緒申鐃緒申 No.4

鐃緒申鐃緒申鐃塾テ￥申鐃緒申:

$\fbox{群の表現の例}$

鐃瞬器申表鐃緒申
$\mathfrak{S}_n$ 鐃緒申鐃緒申分鐃緒申鐃緒申鐃出わ申鐃銃￥申鐃緒申表鐃緒申鐃緒申鐃緒申鐃塾よう鐃緒申鐃緒申泙襦�

$\displaystyle \sigma.e_i=e_{\sigma(i)}$
鐃緒申鐃緒申表鐃緒申鐃緒申鐃緒申鐃瞬器申表鐃緒申鐃夙呼ぶ￥申
鐃緒申鐃緒申表鐃緒申
鐃緒申鐃緒申鐃緒申鐃銃の醐申鐃緒申鐃出わ申鐃銃￥申鐃緒申鐃出縁申鐃緒申鐃緒申鐃緒申鐃� 鐃塾逸申弔鐃� 表鐃緒申鐃緒申鐃叔わ申鐃暑。鐃緒申鐃緒申鐃� 鐃塾刻申鐃緒申表鐃緒申鐃夙わ申鐃緒申鐃緒申
鐃緒申鐃藷式わ申鐃術わ申鐃銃削申鐃緒申鐃宿緒申鐃�
鐃緒申鐃緒申侶鐃� 鐃緒申表鐃緒申 $\rho:G\to GL_n(K)$ 鐃緒申与鐃緒申鐃緒申鐃銃わ申鐃緒申箸鐃緒申法鐃� $\operatorname{det}(\rho): G\to {\operatorname{GL}}_1(K)(=K^{\times})$ 鐃緒申

$\displaystyle \operatorname{det}(\rho)(g)=\operatorname{det}(\rho(g))$
鐃緒申鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。

鐃緒申鐃緒申鐃縦わ申鐃緒申里茲�申法鐃� 鐃緒申鐃緒申表鐃緒申 $\rho:G\to GL_n(K)$ 鐃塾なわ申鐃祝は￥申 $\rho$ 鐃緒申単鐃粛でなわ申鐃緒申里發�申襦�

鐃緒申鐃� 4.1 $\rho$ 鐃緒申単鐃粛でわ申鐃緒申茲�申鐃宿緒申鐃緒申里鐃緒申箸鐃� 鐃緒申造鐃�表鐃緒申鐃夙わ申屐鐃�

鐃瞬器申表鐃緒申鐃淑ど￥申鐃緒申鐃殉までに挙げわ申表鐃緒申鐃熟刻申鐃緒申鐃緒申鐃淑�申鐃� 0 鐃緒申鐃緒申鐃緒申鐃出わ申鐃緒申覆鐃緒申茲�申覆鐃塾ばわ申鐃緒申鐃緒申辰鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃叔わ申鐃緒申鐃薯くなわ申鐃緒申鐃渋は件申鐃緒申鐃緒申鐃銃わ申表鐃緒申鐃熟￥申鐃緒申則表鐃緒申鐃薯うまわ申鐃緒申分鐃緒申廚鐃緒申襪鰹申箸砲鐃緒申鐃緒申鐃緒申鐃暑こ鐃夙わ申鐃塾わ申鐃銃わ申鐃暑。

鐃緒申分鐃緒申廚覆匹両楮戮呂鐃獣と醐申旅峙鐃緒申能劼戮襪鰹申箸砲鐃緒申董鐃� 鐃緒申鐃緒申鐃塾講居申鐃叔わ申 $\frak S_3$ 鐃緒申鐃瞬器申表鐃緒申鐃緒申鐃初、如鐃緒申鐃緒申鐃藷次わ申表鐃緒申鐃緒申鐃緒申襪�申砲弔鐃緒申峠劼戮襦�

鐃緒申鐃緒申 4.1

$\rho$ 鐃緒申鐃緒申造鐃宿緒申鐃緒申任鐃緒申襪鰹申箸函鐃� $\operatorname{Ker}(\rho)=e$ 鐃緒申同鐃粛でわ申鐃暑。
鐃緒申則表鐃緒申鐃緒申必鐃緒申鐃緒申造鐃宿緒申鐃緒申任鐃緒申襦�

鐃緒申鐃緒申 4.1 鐃瞬居申鐃緒申鐃緒申砲覆鐃獣て￥申

鐃緒申鐃緒申則表鐃緒申鐃緒申分鐃薯しわ申

鐃緒申鐃藷次わ申表鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申 4.2 $\frak A_4$ 鐃塾一次鐃緒申表鐃緒申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申表鐃緒申鐃叔なわ申鐃緒申里鐃� 鐃緒申銚鐃緒申佞鐃緒申茵� (鐃述ワ申鐃�: $\frak A_4$ 鐃緒申鐃緒申分鐃緒申鐃塾わ申鐃緒申鐃緒申鐃縮随申

鐃塾わ申里鐃緒申鐃緒申鐃緒申鐃淑�申鐃緒申砲覆襦� 鐃緒申鐃緒申鬚Δ泙鐃緒申鐃緒申僂鐃緒申襦�)

鐃緒申鐃緒申 4.3 鐃緒申則表鐃緒申鐃緒申鐃瞬器申表鐃緒申鐃塾逸申鐃叔わ申鐃暑こ鐃夙わ申鐃緒申鬚△鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃�

平鐃緒申15年5鐃緒申12鐃緒申