Irreducible representations of the crystallization of the quantized function algebras $C(\operatorname{SU}_{q}(n+1))$

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The crystallization of the C^{*} -algebras C(\operatorname{SU}_{q}(n+1)) was introduced by Giri and Pal in [Proc. Indian Acad. Sci. Math. Sci. 134 (2024), article no. 30] as a C^{*} -algebra C(\operatorname{SU}_{0}(n+1)) given by a finite set of generators and relations. Here we study the representations of the C^{*} -algebra C(\operatorname{SU}_{0}(n+1)) and prove a factorization theorem for its irreducible representations. This leads to a complete classification of all irreducible representations of this C^{*} -algebra. As an important consequence, we prove that all the irreducible representations of C(\operatorname{SU}_{0}(n+1)) arise exactly as q\to 0+ limits of the irreducible representations of C(\operatorname{SU}_{q}(n+1)) . We also present a few other important corollaries of the classification theorem.