Adapting Soibelman’s highest-weight methods to classify irreducible representations of C0(SU(n+1))

Determine whether Soibelman’s highest-weight module approach for classifying irreducible representations of the quantized function algebras C(Kq) can be modified to provide a classification of the irreducible representations of the crystallized C*-algebra C0(SU(n+1)).

Background

In the nonzero q setting, Soibelman’s theory classifies irreducible representations of C(Kq) using highest-weight modules. The present paper achieves a complete classification of irreducible representations for the crystallized algebra C0(SU(n+1)) via operator-theoretic methods rather than highest-weight techniques.

The authors explicitly note uncertainty about whether Soibelman’s methodology can be adapted to the q→0 crystallized setting. Resolving this would connect the classical q≠0 representation-theoretic framework with the crystal limit and potentially streamline or unify classification tools across q.