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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.

##### 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
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##### References:
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