Symmetric quantum Weyl algebras

Rafael Díaz[1]; Eddy Pariguan[2]

  • [1] Instituto Venezolano de Inves- tigaciones Científicas Departamento de Matemáticas Altos de Pipe. Caracas 21827 Venezuela
  • [2] Universidad Central de Venezue- la Departamento de Matemáticas Los Chaguaramos Caracas 1020 Venezuela

Annales mathématiques Blaise Pascal (2004)

  • Volume: 11, Issue: 2, page 187-203
  • ISSN: 1259-1734

Abstract

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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.

How to cite

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Díaz, Rafael, and Pariguan, Eddy. "Symmetric quantum Weyl algebras." Annales mathématiques Blaise Pascal 11.2 (2004): 187-203. <http://eudml.org/doc/10505>.

@article{Díaz2004,
abstract = {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.},
affiliation = {Instituto Venezolano de Inves- tigaciones Científicas Departamento de Matemáticas Altos de Pipe. Caracas 21827 Venezuela; Universidad Central de Venezue- la Departamento de Matemáticas Los Chaguaramos Caracas 1020 Venezuela},
author = {Díaz, Rafael, Pariguan, Eddy},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
month = {7},
number = {2},
pages = {187-203},
publisher = {Annales mathématiques Blaise Pascal},
title = {Symmetric quantum Weyl algebras},
url = {http://eudml.org/doc/10505},
volume = {11},
year = {2004},
}

TY - JOUR
AU - Díaz, Rafael
AU - Pariguan, Eddy
TI - Symmetric quantum Weyl algebras
JO - Annales mathématiques Blaise Pascal
DA - 2004/7//
PB - Annales mathématiques Blaise Pascal
VL - 11
IS - 2
SP - 187
EP - 203
AB - 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.
LA - eng
UR - http://eudml.org/doc/10505
ER -

References

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  2. Christian Kassel, Quantum groups, (1995), Springer-Velarg, New York Zbl0808.17003MR1321145
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  7. Peter Doubilet, On the foundations of combinatorial theory. VII: Symmetric functions through the theory of distribution and occupancy, Gian-Carlo Rota on Combinatorics. Introductory papers and commentaries (1995), 402-422 
  8. Rafael Díaz, Eddy Pariguan, Quantum symmetric functions, (2003) Zbl1093.53096
  9. Rafael Díaz, Eddy Pariguan, Super, quantum and non-commutative species, (2004) Zbl1239.16001
  10. Rajesh Gopakumar, Shiraz Minwalla, Andrew Strominger, Noncommutative Solitons, J. High Energy Phys. JHEP 05-020 (2000) Zbl0989.81612MR1768736
  11. A.I. Solomon, Phys.Lett. A 196 (1994) 
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  13. Victor Kac, Pokman Cheung, Quantum Calculus, (2002), Springer-Velarg, New York Zbl0986.05001MR1865777

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