Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
Abstract
Description
The vector fields of the quantum Lie algebra are described for the quantum groups $GL_q(N), SL_q(N)$ and $SO_q(N)$ as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms $SU_q(N)$ and $SO_q(N,R)$ are discussed in detail.
16 pages, Latex, no figures, to appear in the Proceedings of the XX International Conference on Group Theory Methods in Physics, Toyonaka, Japan (1994)
16 pages, Latex, no figures, to appear in the Proceedings of the XX International Conference on Group Theory Methods in Physics, Toyonaka, Japan (1994)