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Title: GL(3,C) invariance of type B 3-fold supersymmetric systems

Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear transformations. In particular, we prove explicitly that the parameter space is transformed as an adjoint representation of it and that every coefficient of the characteristic polynomial appeared in 3-fold superalgebra is algebraic invariants. In the type A case, it includes as a subgroup the GL(2,C) projective transformation studied in the literature. We argue that any N-fold supersymmetric system has a GL(N,C) invariance for an arbitrary integral N.
Authors:
 [1]
  1. Department of Physics, Faculty of Science, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610 (Japan)
Publication Date:
OSTI Identifier:
22251554
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GAUGE INVARIANCE; HAMILTONIANS; MATHEMATICAL SOLUTIONS; POLYNOMIALS; SUPERSYMMETRY; TRANSFORMATIONS