Geodesic
Global Lie Symmetries of the Heat and Schrödinger Equation
Journal of Lie theory, Tome 20 (2010) no. 3, pp. 543-58
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We examine solutions to a family of differential equations, including the heat and Schrödinger 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 Schrödinger equation.
Classification : 58J70, 22E45, 22E70, 35A30
Mots-clés : Heat equation, Schroedinger equation, oscillator representation 
@article{JLT_2010_20_3_JLT_2010_20_3_a6,
     author = {M. R. Sepanski and R. J. Stanke},
     title = {Global {Lie} {Symmetries} of the {Heat} and {Schr\"odinger} {Equation}},
     journal = {Journal of Lie theory},
     pages = {543--58},
     year = {2010},
     volume = {20},
     number = {3},
     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 Schrödinger 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/