Quasi-Exactly Solvable Models and W-Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9602076,
title = {Quasi-Exactly Solvable Models and W-Algebras},
author = {A. G. Ushveridze},
journal= {arXiv preprint arXiv:hep-th/9602076},
year = {2008}
}
Comments
LaTeX, 14 pages. This is a new version with Acknowledgements which I have forgotten to include into the old one