Search: MSC category 81R05
( Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70] )
1. CJM 1998 (vol 50 pp. 1298)
||Imprimitively generated Lie-algebraic Hamiltonians and separation of variables |
Turbiner's conjecture posits that a Lie-algebraic Hamiltonian
operator whose domain is a subset of the Euclidean plane admits a
separation of variables. A proof of this conjecture is given in
those cases where the generating Lie-algebra acts imprimitively.
The general form of the conjecture is false. A counter-example is
given based on the trigonometric Olshanetsky-Perelomov potential
corresponding to the $A_2$ root system.
Categories:35Q40, 53C30, 81R05