1996/11/30 by Harold Steinacker · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #hep-th #math.QA #q-alg
paper · pdf · doi:10.1007/s002200050315
published as Commun.Math.Phys. 192 (1998) 687-706 · More systematic proof of statements on the structure of irreps, some typos corrected. 25 pages LaTeX, 4 figures included using epsf. To appear in Comm. Math. Phys
arxiv created 1997/08/02 · openalex publication_date 1998/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We study irreducible unitary \reps of Uq(SO(2,1)) and Uq(SO(2,3)) for q a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are found for q = ei π/M, with M being large enough. In the "massless" case with spin bigger than or equal to 1 in 4 dimensions, they are unitarizable only after factoring out a subspace of "pure gauges", as classically. A truncated associative tensor product describing unitary many-particle representations is defined for q = eiπ/M.