Id Notation Reducementals Architecture 1 ${\mathbb{U}}_{1}.{\mathbb{U}}_{1}$ $\left\{\begin{array}{cc}1& 1\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+1\\ n-1\end{array}\right)& \left(\begin{array}{c}n\\ n-2\end{array}\right)\end{array}\right\}$ $\delta =2;\omega =2;g=0$ 2 ${\mathbb{U}}_{1}.{\mathbb{U}}_{2}$ $\left\{\begin{array}{cc}1& 2\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \left(\begin{array}{c}n+1\\ n-2\end{array}\right)\end{array}\right\}$ $\delta =3;\omega =2;g=0$ 3 ${\mathbb{U}}_{1}.{\mathbb{U}}_{3}$ $\left\{\begin{array}{cc}1& 3\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \left(\begin{array}{c}n+2\\ n-2\end{array}\right)\end{array}\right\}$ $\delta =4;\omega =2;g=0$ 4 ${\mathbb{U}}_{2}.{\mathbb{U}}_{2}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}4& 1\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \left(\begin{array}{c}n+1\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =3;\omega =3;g=0$ 5 ${\mathbb{U}}_{2}.{\mathbb{U}}_{3}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}6& 3\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+4\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-2\end{array}\right)& \left(\begin{array}{c}n+2\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =4;\omega =3;g=0$ 6 ${\mathbb{U}}_{2}.{\mathbb{U}}_{4}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}8& 6\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+5\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-2\end{array}\right)& \left(\begin{array}{c}n+3\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =4;\omega =3;g=0$ 7 ${\mathbb{U}}_{2}.{\mathbb{U}}_{5}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}10& 10\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+6\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+5\\ n-2\end{array}\right)& \left(\begin{array}{c}n+4\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =4;\omega =3;g=0$ 8 ${\mathbb{U}}_{1}.{\mathbb{U}}_{1}.{\mathbb{U}}_{1}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}4& 1\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \left(\begin{array}{c}n\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =3;\omega =3;g=0$ 9 ${\mathbb{U}}_{1}.{\mathbb{U}}_{1}.{\mathbb{U}}_{2}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}7& 4\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \left(\begin{array}{c}n+1\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =4;\omega =3;g=0$ 10 ${\mathbb{U}}_{1}.{\mathbb{U}}_{1}.{\mathbb{U}}_{3}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}10& 9\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+4\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-2\end{array}\right)& \left(\begin{array}{c}n+2\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =5;\omega =3;g=0$ 11 ${\mathbb{U}}_{1}.{\mathbb{U}}_{1}.{\mathbb{U}}_{4}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}13& 16\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+5\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-2\end{array}\right)& \left(\begin{array}{c}n+3\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =5;\omega =3;g=0$ 12 ${\mathbb{U}}_{1}.{\mathbb{U}}_{3}.{\mathbb{U}}_{3}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}24& \begin{array}{cc}72& \begin{array}{cc}24& 3\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+5\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-2\end{array}\right)& \left(\begin{array}{c}n+3\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =7;\omega =5;g=0$ 13 ${\mathbb{U}}_{2}.{\mathbb{U}}_{3}.{\mathbb{U}}_{3}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}39& \begin{array}{cc}204& \begin{array}{cc}244& \begin{array}{cc}204& \begin{array}{cc}39& 1\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+7\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+6\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+5\\ n-3\end{array}\right)& \left(\begin{array}{c}n+3\\ n-3\end{array}\right)\end{array}\end{array}\end{array}\right\}\end{array}$ $\delta =8;\omega =7$