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

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Central European Journal of Mathematics

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.

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Authors and Affiliations

  1. Department of Mathematics, Baylor University, One Bear Place 97328, Waco, 76643, USA

    Jose Franco

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  1. Jose Franco
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Correspondence to Jose Franco.

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Franco, J. Global \(\widetilde{SL(2,R)}\) representations of the Schrödinger equation with singular potential. centr.eur.j.math. 10, 927–941 (2012). https://doi.org/10.2478/s11533-012-0040-8

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  • DOI: https://doi.org/10.2478/s11533-012-0040-8

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