A two-parametric deformation of U[sl(2)], its representations and complex "spin"

2005/06/27 by N. Anh Ky, Nguyen Anh Ky, Ky, Nguyen Anh +2
Mathematics · Physics and Astronomy · #17B37 #81R50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Representation Theory (math.RT) #hep-th #math-ph #math.MP #math.QA #math.RT #msc:17B37 #msc:81R50 #nlin.SI #quant-ph

paper · pdf · doi:10.48550/arxiv.math/0506539

LaTeX, 7 pages, no figure. In v2: Minor corrections; discussions and references added; line spacing reduced

openalex publication_date 2005/06/27 · arxiv created 2005/07/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as U_pq[sl(2)] admits a class of infinite-dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters. Interestingly that finite-dimensional representations of U_pq[sl(2)] allow arbitrary complex "spins" (i.e., not necessary they to be integral or half-integral numbers), unlike those in the classical and one-parametric deformation cases.

Related

• Some deformations of U[sl(2)] and their representations
• Discrete series of representations for the modular double of U_q(sl(2,R))
• Representations of Multiparameter Quantum Groups
• On the Drinfeld Twist for Quantum sl(2)
• Representations and Classification of the compact quantum groups U_q(2) for complex deformation parameters