Cluster realization of positive representations of split real quantum\n Borel subalgebra

2017/11/30 by Ivan Chi-Ho Ip, Ip, Ivan Chi-Ho
Mathematics · Physics and Astronomy · #22D25 #81R50 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum many-body systems #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1712.00013

openalex publication_date 2017/11/30 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In our previous work, we studied the positive representations of split real\nquantum groups \U_q\q( mathfrakg_\ℝ) restricted\nto its Borel part, and showed that they are closed under taking tensor\nproducts. However, the tensor product decomposition was only constructed\nabstractly using the GNS-representation of a C^*-algebraic version of the\nDrinfeld-Jimbo quantum groups. In this paper, using the recently discovered\ncluster realization of quantum groups, we write down the decomposition\nexplicitly by realizing it as a sequence of cluster mutations in the\ncorresponding quiver diagram representing the tensor product.\n

Related

• Cluster Realization of U_q( mathfrakg) and Factorization of the\n Universal R-Matrix
• On tensor products of positive representations of split real quantum Borel subalgebra U_qq(b_R)
• Positive representations of split real quantum groups and future perspectives
• A cluster realization of U_q(\mathfraksl_n) from quantum character varieties
• Quantum cluster mutations and reduced word graphs