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Realization of U-q(so(N)) within the differential algebra on R-q(N)

Jun, 1993
26 pages
Published in:
  • Commun.Math.Phys. 169 (1995) 475-500
e-Print:
DOI:
Report number:
  • SISSA-90-93-EP
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199419992004200920122103
Abstract: (arXiv)
We realize the Hopf algebra Uq−1(so(N))U_{q^{-1}}(so(N)) as an algebra of differential operators on the quantum Euclidean space RqN{\bf R}_q^N. The generators are suitable q-deformed analogs of the angular momentum components on ordinary RN{\bf R}^N. The algebra Fun(RqN)Fun({\bf R}_q^N) of functions on RqN{\bf R}_q^N splits into a direct sum of irreducible vector representations of Uq−1(so(N))U_{q^{-1}}(so(N)); the latter are explicitly constructed as highest weight representations.
Note:
  • 26 pages, 1 figure