Yang, Qunfeng; Deng, Minghua Tensor product representation and quantum symmetry. (Chinese. English summary) Zbl 0865.17013 Adv. Math., Beijing 24, No. 6, 532-539 (1995). 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 Keywords:quantum symmetry; quantum anti-symmetry; \(q\)-boson; \(q\)-fermion; quantum symmetric group; \(q\)-oscillator; \(q\)-spinor representation; tensor product; standard representation PDFBibTeX XMLCite \textit{Q. Yang} and \textit{M. Deng}, Adv. Math., Beijing 24, No. 6, 532--539 (1995; Zbl 0865.17013)