Irreducible representations of the crystallization of the quantized function algebras C(SU_q(n+1))

2024/02/14 by Manabendra Giri, Giri, Manabendra, Arup Kumar Pal +1
Mathematics · #20G42 #46L67 #58B32 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2402.09347

openalex publication_date 2024/02/14 · openalex created_date 2024/02/16 · openalex updated_date 2026/07/28

Abstract

Crystallization of the C^*-algebras C(SU_q(n+1)) was introduced by Giri & Pal as a C^*-algebra C(SU₀(n+1)) given by a finite set of generators and relations. Here we study representations of the C^*-algebra C(SU₀(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(SU₀(n+1)) arise exactly as q→ 0+ limits of irreducible representations of C(SU_q(n+1)). We also present a few other important corollaries of the classification theorem.

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