On representations of the crystallization of the quantized function algebra C(SUq(n + 1))

Abstract

The crystal limit C(K0) of the $q$-family of C*-algebras C(Kq) was introduced by Giri & Pal for all K=SU(n+1), n\geq 2. This article aims to prove that the crystal limits C(K0) have the property that the representations of C(Kq) give rise to the representations of the crystallized algebra C(K0) by sending generators of C(K0) to the limit of (scaled) generators of C(Kq)$ and every representation of C(K0) occurs in this way. This work addresses a question raised by Giri & Pal in \cite{GirPal-2024}. As a consequence, one can realize C(K0) as the C*-algebra generated by the limit operators of faithful representations of C(Kq).