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Global S L ( 2 , R ) ˜ representations of the Schrödinger equation with singular potential

Jose Franco (2012)

Open Mathematics

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 S L ( 2 , ) ˜ . 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 S L ( 2 , ) ˜ ⋉ H 3, where H...

Lie algebroids and mechanics

Paulette Libermann (1996)

Archivum Mathematicum

We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold M ; the set of units is the zero section identified with the manifold M . We study the Legendre transformation on Lie algebroids.

Lie symmetry of a class of nonlinear boundary value problems with free boundaries

Roman Cherniha, Sergii Kovalenko (2011)

Banach Center Publications

A class of (1 + 1)-dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie symmetry method. A new definition of invariance in Lie's sense for BVP is presented and applied to the class of BVPs in question.

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