Realization of $U_q(so(N))$ within the differntial algebra on ${\bf R}_q^N$

Details Realization of $U_q(so(N))$ within the differntial algebra on ${\bf R}_q^N$ Realization of $U_q(so(N))$ within the differntial algebra on ${\bf R}_q^N$

1994-03-04

arxiv.org/abs/hep-th/9403033v1

Commun.Math.Phys. 169 (1995) 475-500

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 1 figure

Scientific paper

10.1007/BF02099309

We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space ${\bf R}_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary ${\bf R}^N$. The algebra $Fun({\bf R}_q^N)$ of functions on ${\bf R}_q^N$ splits into a direct sum of irreducible vector representations of $U_{q^{-1}}(so(N))$; the latter are explicitly constructed as highest weight representations.

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