%0 Journal Article
%T The Heun Equation and Generalized Sl(2) Algebra
%A Sadeghi, J.
%A Vaezi, A.
%A Larijani, F.
%J Journal of Mathematics and Computer Science
%D 2016
%V 16
%N 1
%@ ISSN 2008-949X
%F Sadeghi2016
%X In this paper, first we introduce the Heun equation. In order to solve such equation we show the
generators of generalized \(sl(2)\). Second, we arrange the Heun equation in terms of new operators
formed of generalized \(sl(2)\) generators and it's commutator relation. Here, instead of \(J^+(r), J^-(r)\) and
\(J^0\) we use the \(P^+(r), P^-(r)\) and \(P^0(r)\) as operators of generalized sl(2) algebra. This correspondence
gives us opportunity to arrange the parameters \(\alpha\) and \(\beta\) in \(P^0(r)\). Also, the commutator of such
operators leads us to have generalized \(sl(2)\) algebra. Also, we obtain the Casimir operators and
show that it corresponds to \(P^+, P^-\) and some constants. These operators lead to deform the
structure of generalized \(sl(2)\) algebra in the Heun equation. Finally, we investigate the condition for
exactly and quasi-exactly solvable system with constraint on the corresponding operators \(P^+\) and \(P^-\).
%9 journal article
%R 10.22436/jmcs.016.01.08
%U http://dx.doi.org/10.22436/jmcs.016.01.08
%P 77-80