We identify the "dynamical algebras" ℍD of the D-dimensional hydrogen atom as positive subalgebras of twisted and untwisted affine Kac-Moody algebras: For odd D ≥ 5 we obtain ℍ2l+1 ≃ D(2)+l+1. But for even D ≥ 6, ℍ2l is a parabolic subalgebra of B(1)l. ℍ4 is a parabolic subalgebra of C(1)2, ℍ3 ≃ D(2)+2 ≃ A(1)+1, while ℍ2 is isomorphic to the Borel subalgebra of A(1)1. Along the way we prove a theorem on the untwisting of positive subalgebras of twisted affine algebras, and introduce generalized Dynkin diagrams which enable us to represent graphically automorphisms and parabolic subalgebras of finite and affine algebras.
|Number of pages||10|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - 16 Apr 1998|
ASJC Scopus subject areas
- Nuclear and High Energy Physics