Properties

Label 1.4.2.4.2a
  
Name \(F_{a,b}\)
Weight 1
Degree 4
Real dimension 2
Components 4
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)\times\mathrm{U}(1)\)
Component group \(C_2^2\)

Learn more about

Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$2$
Components:$4$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{U}(1)\times\mathrm{U}(1)$
Index:$4$
$\mathbb{R}$-dimension:$2$
Description:$\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A,B\in \mathrm{U}(1)\right\}$

Component Group

Name:$C_2^2$
Order:$4$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$F_a$, $F_{ab}$
Minimal Supergroups:

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $110$ $0$ $1260$ $0$ $16002$ $0$ $213906$
$a_2$ $1$ $2$ $5$ $14$ $49$ $202$ $944$ $4720$ $24553$ $130658$ $705880$ $3855040$ $21232468$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{4}$
$\mathrm{P}[a_2=2]=\frac{3}{4}$