Letters in Mathematical Physics

, Volume 32, Issue 1, pp 37–44 | Cite as

Symmetries of theq-difference heat equation

  • Roberto Floreanini
  • Luc Vinet


The symmetry operators of aq-difference analog of the heat equation in one space dimension are determined. They are seen to generate aq-deformation of the semidirect product of sl(2, ℝ) with the three-dimensional Weyl algebra. It is shown that this algebraic structure is preserved if differentq-analogs of the heat equation are considered. The separation of variables associated to the dilatation symmetry is performed and solutions involving discreteq-Hermite polynomials are obtained.

Mathematics Subject Classifications (1991)

39-XX 81-XX 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gasper, G. and Rahman, M.,Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.Google Scholar
  2. 2.
    Floreanini, R. and Vinet, L., Quantum algebras andq-special functions,Ann. Phys. 221 (1993), 53–79.Google Scholar
  3. 3.
    Miller, W.,Symmetry and Separation of Variables, Addison-Wesley, Reading, Mass, 1977.Google Scholar
  4. 4.
    Blumen, G. and Cole, J., The general similarity solution of the heat equation,J. Math. Mech. 18, 1025–1042 (1969); Kalnins, E. and Miller, W., Lie theory and separation of variables, 5: The equationsiU t +U xx = 0 andiU t +U xxc/x 2 U = 0,J. Math. Phys. 15, 1728–1737 (1974).Google Scholar
  5. 5.
    Al-Salam, W. A. and Carlitz, L., Some orthogonalq-polynomials,Math. Nachr. 30, 47–61 (1965).Google Scholar
  6. 6.
    Floreanini, R. and Vinet, L., Quantum symmetries ofq-difference equations, CRM-preprint, 1994.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Roberto Floreanini
    • 1
  • Luc Vinet
    • 2
  1. 1.Istituto Nazionale di Fisica NucleareSezione di Trieste, Dipartimento di Fisica Teorica, Università di TriesteTriesteItaly
  2. 2.Centre de recherches mathématiquesUniversité de MontréalMontréalCanada

Personalised recommendations