Find non-classical property (T) discrete quantum groups with large finite-dimensional coideals

Construct non-classical discrete quantum groups with property (T) that admit finite-dimensional coideals of large (e.g., arbitrarily large) dimension, enabling the quantum Schreier graph expander construction based on coideals.

Background

Quantum Schreier graph expanders in this work arise from coideals M \subseteq \ell^\infty(\hat{\mathbb G}). To obtain expander families, one needs sequences of finite-dimensional coideals with dimensions growing without bound.

While the paper develops the framework and proves spectral gap results, concrete non-classical examples with suitably large finite-dimensional coideals are not currently known; identifying such discrete quantum groups is necessary to instantiate the construction beyond classical cases.