Id

AC Symbols

Reducementals

Architecture

1

${\mathbb{U}}_1\text{R}1\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\left\{\begin{array}{cc}1& \begin{array}{cc}5& 2\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \left(\begin{array}{c}n+1\\ n-3\end{array}\right)\end{array}\end{array}\right\}$

$\delta =4;\omega =3;g=0$

2

${\mathbb{U}}_2\text{R}1\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\left\{\begin{array}{cc}1& \begin{array}{cc}9& \begin{array}{cc}9& 1\end{array}\end{array}\end{array}\right\}\circ \left\{\begin{array}{cc}\left(\begin{array}{c}n+4\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-3\end{array}\right)& \left(\begin{array}{c}n+1\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$

$\delta =5;\omega =4;g=0$

3

${\mathbb{U}}_3\text{R}1\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\left\{\begin{array}{cc}1& \begin{array}{cc}13& \begin{array}{cc}21& 5\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+5\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-3\end{array}\right)& \left(\begin{array}{c}n+2\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$

$\delta =6;\omega =4;g=0$

4

${\mathbb{U}}_4\text{R}1\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\left\{\begin{array}{cc}1& \begin{array}{cc}17& \begin{array}{cc}38& 14\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+6\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+5\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-3\end{array}\right)& \left(\begin{array}{c}n+3\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$

$\delta =7;\omega =4;g=0$

5

${\mathbb{U}}_1\text{R2}\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\left\{\begin{array}{cc}1& \begin{array}{cc}6& 3\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+4\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-2\end{array}\right)& \left(\begin{array}{c}n+2\\ n-3\end{array}\right)\end{array}\end{array}\right\}$

$\delta =5;\omega =3;g=0$

6

${\mathbb{U}}_2\text{R2}\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\left\{\begin{array}{cc}1& \begin{array}{cc}11& \begin{array}{cc}15& 3\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+5\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-3\end{array}\right)& \left(\begin{array}{c}n+2\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$

$\delta =4;\omega =4;g=0$

7

${\mathbb{U}}_3\text{R2}\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}16& \begin{array}{cc}36& \begin{array}{cc}16& 1\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+6\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+5\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+3\\ n-4\end{array}\right)& \left(\begin{array}{c}n+2\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$

$\delta =7;\omega =5;g=0$

8

${\mathbb{U}}_4\text{R2}\left({\mathbb{U}}_1.{\mathbb{U}}_1\right)$

$\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}21& \begin{array}{cc}66& \begin{array}{cc}46& 6\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+7\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+6\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+5\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+4\\ n-4\end{array}\right)& \left(\begin{array}{c}n+3\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$

$\delta =8;\omega =5;g=0$