THE STRUCTURE OF QUASI-EXACTLY SOLVABLE SYSTEMS

The linear, differential operators that preserve the N-dimensional vec tor space whose entries are polynomials of fixed, but arbitrary, degre es in one variable are considered herein. They are relevant for the cl assification of quasi-exactly solvable systems of equations. Generatin g elements are explicitly constructed and rules for ordering their pro ducts are derived. Some examples of equations that can be reduced to s uch systems are discussed. (C) 1995 American Institute of Physics.