Sp(4)_Weyl_Group_Calculations -- Sage

var('a,b')

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(a, b\right)$

t=matrix([[a,0,0,0],[0,b,0,0],[0,0,1/b,0],[0,0,0,1/a]]);t

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} a & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & \frac{1}{b} & 0 \\ 0 & 0 & 0 & \frac{1}{a} \end{array}\right)$

s1=matrix([[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]);s1

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right)$

s2=matrix([[1,0,0,0],[0,0,1,0],[0,-1,0,0],[0,0,0,1]]);s2

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right)$

s1*t*s1.inverse()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} b & 0 & 0 & 0 \\ 0 & a & 0 & 0 \\ 0 & 0 & \frac{1}{a} & 0 \\ 0 & 0 & 0 & \frac{1}{b} \end{array}\right)$

s2*t*s2.inverse()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} a & 0 & 0 & 0 \\ 0 & \frac{1}{b} & 0 & 0 \\ 0 & 0 & b & 0 \\ 0 & 0 & 0 & \frac{1}{a} \end{array}\right)$

s1*s2

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & -1 & 0 & 0 \end{array}\right)$

(s1*s2)*t*(s1*s2).inverse()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} \frac{1}{b} & 0 & 0 & 0 \\ 0 & a & 0 & 0 \\ 0 & 0 & \frac{1}{a} & 0 \\ 0 & 0 & 0 & b \end{array}\right)$

(s1*s2*s1)*t*(s1*s2*s1).inverse()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} \frac{1}{a} & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & \frac{1}{b} & 0 \\ 0 & 0 & 0 & a \end{array}\right)$

(s2*s1*s2)*t*(s2*s1*s2).inverse()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} \frac{1}{b} & 0 & 0 & 0 \\ 0 & \frac{1}{a} & 0 & 0 \\ 0 & 0 & a & 0 \\ 0 & 0 & 0 & b \end{array}\right)$

(s2*s1*s2*s1)*t*(s2*s1*s2*s1).inverse()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} \frac{1}{a} & 0 & 0 & 0 \\ 0 & \frac{1}{b} & 0 & 0 \\ 0 & 0 & b & 0 \\ 0 & 0 & 0 & a \end{array}\right)$

Sp(4)_Weyl_Group_Calculations

1859 days ago by jimlb