Symmetric quantum Weyl algebras
classification
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hep-thquant-ph
keywords
algebraalgebrasweylsymmetricabovearbitrarycombinatorialcoordinates
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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 combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.
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