\begin{figure}[tp]
\centering
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\draw[line width=1.1pt] (2.37,-2.10) -- (3.13,-2.10);
\draw[line width=1.1pt] (2.37,-2.65) -- (3.13,-2.65);
\node[font=\scriptsize,inner sep=0pt] at (0.28,-0.28) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (0.83,-0.83) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (2.48,-1.38) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (3.02,-1.38) {$\frac c2$};
\node[font=\scriptsize,inner sep=0pt] at (1.93,-1.93) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (3.02,-2.43) {$\bullet$};
\node[left,font=\scriptsize] at (0.00,-0.28) {$e_{1}$};
\node[left,font=\scriptsize] at (0.55,-0.83) {$e_{2}$};
\node[left,font=\scriptsize] at (1.10,-1.38) {$e_{3}$};
\node[left,font=\scriptsize] at (1.65,-1.93) {$e_{4}$};
\node[left,font=\scriptsize] at (2.20,-2.48) {$e_{5}$};
\node[above,font=\scriptsize] at (0.28,0) {$e_{2}$};
\node[above,font=\scriptsize] at (0.83,0) {$e_{3}$};
\node[above,font=\scriptsize] at (1.38,0) {$e_{4}$};
\node[above,font=\scriptsize] at (1.93,0) {$e_{5}$};
\node[above,font=\scriptsize] at (2.48,0) {$e_{6}$};
\node[above,font=\scriptsize] at (3.03,0) {$f_{6}$};
\node[below,font=\small] at (1.65,-2.80) {$U_{{\rm Wh},c}$, $\lambda_{{\rm Wh},c}$};
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\node[font=\scriptsize] at (5.62,-0.83) {$0$};
\node[font=\scriptsize] at (6.73,-1.93) {$0$};
\node[font=\scriptsize,inner sep=0pt] at (5.62,-0.28) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (6.18,-0.83) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (6.73,-1.38) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (7.28,-1.93) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (7.28,-2.48) {$\frac c2$};
\node[font=\scriptsize,inner sep=0pt] at (7.83,-2.48) {$\bullet$};
\node[left,font=\scriptsize] at (4.80,-0.28) {$e_{1}$};
\node[left,font=\scriptsize] at (5.35,-0.83) {$e_{2}$};
\node[left,font=\scriptsize] at (5.90,-1.38) {$e_{3}$};
\node[left,font=\scriptsize] at (6.45,-1.93) {$e_{4}$};
\node[left,font=\scriptsize] at (7.00,-2.48) {$e_{5}$};
\node[above,font=\scriptsize] at (5.08,0) {$e_{2}$};
\node[above,font=\scriptsize] at (5.62,0) {$e_{3}$};
\node[above,font=\scriptsize] at (6.17,0) {$e_{4}$};
\node[above,font=\scriptsize] at (6.72,0) {$e_{5}$};
\node[above,font=\scriptsize] at (7.28,0) {$e_{6}$};
\node[above,font=\scriptsize] at (7.83,0) {$f_{6}$};
\node[below,font=\small] at (6.45,-2.80) {$U_{\rm alt}$, $\lambda_{{\rm alt},c}$};
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\node[font=\scriptsize] at (9.88,-0.28) {$a$};
\node[font=\scriptsize] at (10.97,-1.38) {$a$};
\node[font=\scriptsize] at (12.08,-2.48) {$a$};
\node[font=\scriptsize,inner sep=0pt] at (10.43,-0.28) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (10.43,-0.83) {$-a$};
\node[font=\scriptsize,inner sep=0pt] at (10.97,-0.83) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (11.53,-1.38) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (11.53,-1.93) {$-a$};
\node[font=\scriptsize,inner sep=0pt] at (12.08,-1.93) {$\bullet$};
\node[font=\scriptsize,inner sep=0pt] at (12.62,-2.48) {$\bullet$};
\node[left,font=\scriptsize] at (9.60,-0.28) {$e_{1}$};
\node[left,font=\scriptsize] at (10.15,-0.83) {$e_{2}$};
\node[left,font=\scriptsize] at (10.70,-1.38) {$e_{3}$};
\node[left,font=\scriptsize] at (11.25,-1.93) {$e_{4}$};
\node[left,font=\scriptsize] at (11.80,-2.48) {$e_{5}$};
\node[above,font=\scriptsize] at (9.88,0) {$e_{2}$};
\node[above,font=\scriptsize] at (10.42,0) {$e_{3}$};
\node[above,font=\scriptsize] at (10.97,0) {$e_{4}$};
\node[above,font=\scriptsize] at (11.53,0) {$e_{5}$};
\node[above,font=\scriptsize] at (12.07,0) {$e_{6}$};
\node[above,font=\scriptsize] at (12.62,0) {$f_{6}$};
\node[below,font=\small] at (11.25,-2.80) {$U_{\rm corr}$, $\Lambda_c$};
\end{tikzpicture}
\caption{Three of the subgroups of $U_{\rm last}^0$ of
Table~\ref{rw:tab:even-descent-route}, with their characters, for
$n=3$ and $m=6$. The cells are the entries $g_{i,j}$ in the rows of
$e_1,\ldots,e_5$ and the columns of $e_2,\ldots,e_6$ and $f_6$; the
remaining root subgroups of $U_{\rm last}^0$ belong to the three
groups, and the characters are trivial on them. A shaded cell is an entry subject to a condition: it
vanishes, or it has the common value $a$, or it is one of two entries
joined by a bar, which satisfy $L_i=0$. The symbol in a cell is the
coefficient of that entry in the character, a dot standing for $1$;
the character $\Lambda_c$ contains in addition the term
$\tfrac c2a$. In $U_{{\rm Wh},c}$ the character follows the two chains
$e_1,e_2,e_3$ and $e_4,e_5$. Row separation, interleaving and the
isometry of step~2 of the proof of
Lemma~\ref{fl:lem:even-period-to-generic}, which sends
$e_1,e_2,e_3$ to $e_1,e_3,e_5$ and $e_4,e_5$ to $e_2,e_4$ and
exchanges $e_6$ and $f_6$, carry it to the second diagonal of
$U_{\rm alt}$.}
\label{rw:fig:even-groups}
\end{figure}