Symmetric quantum Weyl algebras
Annales Mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 187-203.

We study the symmetric powers of four algebras: q-oscillator algebra, q-Weyl algebra, h-Weyl algebra and U(𝔰𝔩 2 ). We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.

@article{AMBP_2004__11_2_187_0,
     author = {D\'\i az, Rafael and Pariguan, Eddy},
     title = {Symmetric quantum Weyl algebras},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {187--203},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {11},
     number = {2},
     year = {2004},
     doi = {10.5802/ambp.192},
     mrnumber = {2109607},
     zbl = {02205936},
     language = {en},
     url = {www.numdam.org/item/AMBP_2004__11_2_187_0/}
}
Díaz, Rafael; Pariguan, Eddy. Symmetric quantum Weyl algebras. Annales Mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 187-203. doi : 10.5802/ambp.192. http://www.numdam.org/item/AMBP_2004__11_2_187_0/

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