Hecke Parabolic Induction and Symmetrizing Traces — Examples

Calculate parabolic induction from rank one into S3, its two-sided conventions, and dual trace bases. A perfect symmetrizing form alone does not imply semisimplicity; supply a nonsemisimple specialization illustrating this.

These are planned worked examples and counterexamples for hecke-parabolic-induction-and-symmetrizing-traces, with empty item lists pending normal authoring and proof review. Each example must calculate from the stated hypotheses, and each counterexample must verify both its premises and the failed conclusion. This companion is a dependency leaf and supplies no theorem to another page.