Two-Parameter Quantum Groups and -Matrices: Classical Types

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Martin, Ian, Tsymbaliuk, Alexander
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214100
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Two-Parameter Quantum Groups and -Matrices: Classical Types. Ian Martin and Alexander Tsymbaliuk. SIGMA 21 (2025), 064, 54 pages

We construct finite -matrices for the first fundamental representation of two-parameter quantum groups ᵣ,ₛ() for classical , both through the decomposition of ⊗ into irreducibles ᵣ,ₛ()-submodules as well as by evaluating the universal R-matrix. The latter is crucially based on the construction of...