Properties

Label 1.2.1.2.1a
  
Name \(N(\mathrm{U}(1))\)
Weight 1
Degree 2
Real dimension 1
Components 2
Contained in \(\mathrm{USp}(2)\)
Identity Component \(\mathrm{U}(1)\)
Component group \(C_2\)

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Invariants

Weight:$1$
Degree:$2$
$\mathbb{R}$-dimension:$1$
Components:$2$
Contained in:$\mathrm{USp}(2)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{U}(1)$
Index:$2$
$\mathbb{R}$-dimension:$1$
Description:$\left\{\begin{bmatrix}\alpha&0\\0&\bar\alpha\end{bmatrix}:\alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\}$

Component Group

Name:$C_2$
Order:$2$
Abelian:$\mathrm{True}$
Generators:$\begin{bmatrix}0&1\\1&0\end{bmatrix}$

Subgroups and Supergroups

Maximal Subgroups:$\mathrm{U}(1)$
Minimal Supergroups:

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $3$ $0$ $10$ $0$ $35$ $0$ $126$ $0$ $462$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{2}$