# Global $\tilde{SL(2,R)}$ representations of the Schrödinger equation with singular potential

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 927-941
- ISSN: 2391-5455

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topJose Franco. "Global $\widetilde{SL(2,R)}$ representations of the Schrödinger equation with singular potential." Open Mathematics 10.3 (2012): 927-941. <http://eudml.org/doc/269457>.

@article{JoseFranco2012,

abstract = {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 $\widetilde\{SL(2,\mathbb \{R\})\}$ . 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 $\widetilde\{SL(2,\mathbb \{R\})\}$ ⋉ H 3, where H 3 is the three-dimensional Heisenberg group.},

author = {Jose Franco},

journal = {Open Mathematics},

keywords = {Schrödinger equation; Time-dependent potentials; Lie theory; Representation theory; Globalizations; time-dependent potentials; representation theory; globalizations},

language = {eng},

number = {3},

pages = {927-941},

title = {Global $\widetilde\{SL(2,R)\}$ representations of the Schrödinger equation with singular potential},

url = {http://eudml.org/doc/269457},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Jose Franco

TI - Global $\widetilde{SL(2,R)}$ representations of the Schrödinger equation with singular potential

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 927

EP - 941

AB - 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 $\widetilde{SL(2,\mathbb {R})}$ . 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 $\widetilde{SL(2,\mathbb {R})}$ ⋉ H 3, where H 3 is the three-dimensional Heisenberg group.

LA - eng

KW - Schrödinger equation; Time-dependent potentials; Lie theory; Representation theory; Globalizations; time-dependent potentials; representation theory; globalizations

UR - http://eudml.org/doc/269457

ER -

## References

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