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Symmetric quantum Weyl algebras. (English) Zbl 1136.17304
Summary: We study the symmetric powers of four algebras: \(q\)-oscillator algebra, \(q\)-Weyl algebra, \(h\)-Weyl algebra and \(U({\mathfrak{sl}}_2)\). We provide explicit formulae as well as a combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.

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
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