Quasi-Exactly Solvable Models and W-Algebras

Details Quasi-Exactly Solvable Models and W-Algebras Quasi-Exactly Solvable Models and W-Algebras

1996-02-14

arxiv.org/abs/hep-th/9602076v2

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 14 pages. This is a new version with Acknowledgements which I have forgotten to include into the old one

Scientific paper

The relationship between the quasi-exactly solvable problems and W-algebras is revealed. This relationship enabled one to formulate a new general method for building multi-dimensional and multi-channel exactly and quasi-exactly solvable models with hermitian hamiltonians. The method is based on the use of multi-parameter spectral differential equations constructable from generators of finite-dimensional representations of simple Lie algebras and from generators of the associated W-algebras. It is shown that algebras B(n), C(n+1), D(2n+2) with n>1 and also algebras A(1), G(2), F(4), E(7) and E(8) always lead to models with hermitian hamiltonians. The situation with the remaining algebras A(n), D(2n+3) with n>1 and E(6) is still unclear.

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