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.
1
Dept. of Mathematics, Baylor University, One Bear Place 97328, Waco, TX 76798-7328, U.S.A.
Mark R. Sepanski; Ronald J. Stanke. Global Lie Symmetries of the Heat and Schrödinger Equation. Journal of Lie Theory, Tome 20 (2010) no. 3, pp. 543-580. http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a6/
@article{JOLT_2010_20_3_a6,
author = {Mark R. Sepanski and Ronald J. Stanke},
title = {Global {Lie} {Symmetries} of the {Heat} and {Schr\"odinger} {Equation}},
journal = {Journal of Lie Theory},
pages = {543--580},
year = {2010},
volume = {20},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a6/}
}
TY - JOUR
AU - Mark R. Sepanski
AU - Ronald J. Stanke
TI - Global Lie Symmetries of the Heat and Schrödinger Equation
JO - Journal of Lie Theory
PY - 2010
SP - 543
EP - 580
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a6/
ID - JOLT_2010_20_3_a6
ER -
%0 Journal Article
%A Mark R. Sepanski
%A Ronald J. Stanke
%T Global Lie Symmetries of the Heat and Schrödinger Equation
%J Journal of Lie Theory
%D 2010
%P 543-580
%V 20
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a6/
%F JOLT_2010_20_3_a6
