Unitary quantum groups vs quantum reflection groups

2019/04/29 by Teodor Banica, Banica, Teo
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1904.12647

openalex publication_date 2019/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the intermediate liberation problem for the real and complex unitary and reflection groups, namely O_N,U_N,H_N,K_N. For any of these groups G_N, the problem is that of understanding the structure of the intermediate quantum groups G_N⊂ G_N^×⊂ G_N⁺, in terms of the recently introduced notions of "soft" and "hard" liberation. We solve here some of these questions, our key ingredient being the generation formula H_N^[∞]=, coming via crossed product methods. Also, we conjecture the existence of a "contravariant duality" between the liberations of H_N and of U_N, as a solution to the lack of a covariant duality between these liberations.

Citations

• Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups

Related

• A note on the half-liberation operation
• A Connection between Easy Quantum Groups, Varieties of Groups and Reflection Groups
• Topological generation and matrix models for quantum reflection groups
• Introduction to quantum groups
• Unitary Easy Quantum Groups: the free case and the group case