Type B 3-fold Supersymmetry and Non-polynomial Invariant Subspaces
Abstract
We obtain the most general type B 3-fold supersymmetry by solving directly the intertwining relation. We then show that it is a necessary and sufficient condition for a second-order linear differential operator to have three linearly independent local analytic solutions. We find that there are eight linearly independent non-trivial linear differential operators of this kind. As a by-product, we find new quasi-solvable second-order operators preserving a monomial or polynomial subspace, one in type B, two in type C, and four in type X_2, all of which have been missed in the existing literature. In addition, we show that type A, type B, and type C 3-fold supersymmetries are connected continuously via one parameter. A few new quasi-solvable models are also presented.
Cite
@article{arxiv.1212.0611,
title = {Type B 3-fold Supersymmetry and Non-polynomial Invariant Subspaces},
author = {Toshiaki Tanaka},
journal= {arXiv preprint arXiv:1212.0611},
year = {2013}
}
Comments
32 pages, no figures; 2 sections and 1 appendix added, published version