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Jianrong Li
Jianrong Li
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The longest word in type $A_3$ Weyl group written as a matrix is \begin{align} w_0=\left(\begin{array}{cccc} 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0\\ 0 & 1 & 0 & 0\\ 1 & 0 & 0 & 0 \end{array}\right). \end{align}\begin{align} w_0=s_1s_2s_1=\left(\begin{array}{cccc} 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0\\ 0 & 1 & 0 & 0\\ 1 & 0 & 0 & 0 \end{array}\right). \end{align}

What is the longest word in type $C_2$ Weyl group written in terms of a matrix? In this case, $w_0 = s_1 s_2 s_1 s_2$. How to write $s_1, s_2$ as matrices? Thank you very much.

The longest word in type $A_3$ Weyl group written as a matrix is \begin{align} w_0=\left(\begin{array}{cccc} 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0\\ 0 & 1 & 0 & 0\\ 1 & 0 & 0 & 0 \end{array}\right). \end{align}

What is the longest word in type $C_2$ Weyl group written in terms of a matrix? In this case, $w_0 = s_1 s_2 s_1 s_2$. How to write $s_1, s_2$ as matrices? Thank you very much.

The longest word in type $A_3$ Weyl group written as a matrix is \begin{align} w_0=s_1s_2s_1=\left(\begin{array}{cccc} 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0\\ 0 & 1 & 0 & 0\\ 1 & 0 & 0 & 0 \end{array}\right). \end{align}

What is the longest word in type $C_2$ Weyl group written in terms of a matrix? In this case, $w_0 = s_1 s_2 s_1 s_2$. How to write $s_1, s_2$ as matrices? Thank you very much.

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Jianrong Li
Jianrong Li
  • 6.2k
  • 2
  • 21
  • 34

What is the longest word in type $C_2$ Weyl group written in terms of a matrix?

The longest word in type $A_3$ Weyl group written as a matrix is \begin{align} w_0=\left(\begin{array}{cccc} 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0\\ 0 & 1 & 0 & 0\\ 1 & 0 & 0 & 0 \end{array}\right). \end{align}

What is the longest word in type $C_2$ Weyl group written in terms of a matrix? In this case, $w_0 = s_1 s_2 s_1 s_2$. How to write $s_1, s_2$ as matrices? Thank you very much.