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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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