We study the representation theory of the solution space of the one-dimensional Schrödinger equation with singular potential V λ(x) = λx −2 as a representation of . The subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. By studying the subspace of K-finite vectors in this space, a distinguished family of potentials, parametrized by the triangular numbers is shown to generate a global representation of ⋉ H 3, where H 3 is the three-dimensional Heisenberg group.
@article{bwmeta1.element.doi-10_2478_s11533-012-0040-8,
author = {Jose Franco},
title = {Global $\widetilde{SL(2,R)}$ representations of the Schr\"odinger equation with singular potential},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {927-941},
zbl = {1241.22024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0040-8}
}
Jose Franco. Global $\widetilde{SL(2,R)}$ representations of the Schrödinger equation with singular potential. Open Mathematics, Tome 10 (2012) pp. 927-941. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0040-8/
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