Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations
نویسندگان
چکیده
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n − 2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations. Department of Mathematical Physics, University of Mons, Place du Parc 20, B-7000 MONS, Belgium. Department of Theoretical Physics, University of Lodz, Pomorska 149/153, 90-236 Lodz, Poland, Work supported by Lodz University grants no 458 and no KBN 2 P03B 076 10
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