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Tensor product representation and quantum symmetry. (Chinese. English summary) Zbl 0865.17013

Summary: The authors first define \(U_q(sl_n)\)-polynomials and an \(U_q(sl_n)\)-exterior product by means of the concept of quantum symmetric group. Then they show that either the \(q\)-oscillator or the \(q\)-spinor representation of \(U_q(sl_n)\) is nothing new but respectively the quantum symmetric or anti-symmetric tensor product of the standard representation. This result is in conformity with that in the classical case.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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