Geodesic
Global Lie Symmetries of the Heat and Schr�dinger Equation
Journal of Lie theory, Tome 20 (2010) no. 3, pp. 543-58.

Voir la notice de l'article provenant de la source Heldermann Verlag

We examine solutions to a family of differential equations, including the heat and Schr�dinger equations, that are globally invariant under the action of the corresponding Lie symmetry group. The solution space is realized in a nonstandard parabolically induced representation space as the kernel of a linear combination of Casimir operators of certain distinguished subgroups. Composition series provide a complete description of this kernel and, for special inducing parameters, the oscillator representation is realized in a natural and explicit way as a subspace of solutions to the Schr�dinger equation.
Classification : 58J70, 22E45, 22E70, 35A30
Mots-clés : Heat equation, Schroedinger equation, oscillator representation 
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     author = {M. R. Sepanski and R. J. Stanke },
     title = {Global {Lie} {Symmetries} of the {Heat} and {Schr�dinger} {Equation}},
     journal = {Journal of Lie theory},
     pages = {543--58},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_3_JLT_2010_20_3_a6/}
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M. R. Sepanski; R. J. Stanke . Global Lie Symmetries of the Heat and Schr�dinger Equation. Journal of Lie theory, Tome 20 (2010) no. 3, pp. 543-58. http://geodesic.mathdoc.fr/item/JLT_2010_20_3_JLT_2010_20_3_a6/