Reading the figure
The upper row enlarges K times J to K times P. The lower row induces Lambda to Sigma. Compact induction of Sigma recovers the displayed same candidate.
Mathematical labels
\(\mathcal{N}=K^\times J\)
\(\mathcal{M}=K^\times P\)
\(\Lambda\)
\(\Sigma=\mathrm{Ind}_{\mathcal{N}}^{\mathcal{M}}\Lambda\)
\(\pi\simeq\mathrm{c\!-\!Ind}_{\mathcal{M}}^G\Sigma\)
Selectable labels from the original PDF
Native PDF text retains the figure’s extraction order. Equations and data tables above provide the reading order.
= K × J = K × P Λ Σ = Ind Λ π ≃ c−Ind G Σ
Original figure caption
The noncompact extension \(\Lambda\) is fixed before forming \(\Sigma\).
At both low ranks, \(K^\times\) normalizes \(P\). Put
The subgroup \(\mathcal N\) is normal of index two, \(\Sigma|_P\simeq E\), and \(\Sigma\) is irreducible. Induction in stages proves
Reading the diagram
The parameter, full character, original canonical beta-extension data, central character, and noncompact scalar remain those of the original candidate. The inducing carrier changes.