Symmetric quantum Weyl algebras

Details Symmetric quantum Weyl algebras Symmetric quantum Weyl algebras

2003-11-08

arxiv.org/abs/math/0311128v4

Annales Mathematiques Blaise Pascal. Volume 11 (2004), 187-203

Mathematics

Quantum Algebra

To appear in the Annales Mathematiques Blaise Pascal

Scientific paper

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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