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Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras. (English) Zbl 0701.17008
Q-analogues of Clifford and Weyl algebras are induced. Using these, the spinor and oscillator representations of quantum enveloping algebras of $$A_{N-1}$$, $$B_ N$$, $$C_ N$$, $$D_ N$$ and $$A^{(1)}_{N-1}$$ are constructed and the irreducibility and the unitarity of these representations are discussed.
Reviewer: Li Wanglai

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 15A66 Clifford algebras, spinors
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