Hecke Symmetries and Generic Quantum Schur–Weyl Duality — Examples

Calculate T on a two-dimensional space, all triple-order braid cases, q=1 flip and q=−1 sign distinction, and n=2,N=1 nonfaithfulness. Compute local commutation with each quantum generator before any commutant-equality claim.

These are planned worked examples and counterexamples for hecke-symmetries-and-generic-quantum-schur-weyl-duality, 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.