✦ LIBER ✦

The Lie Algebraic Structure of Differential Operators Admitting Invariant Spaces of Polynomials

✍ Scribed by Frederico Finkel; Niky Kamran

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 269 KB
Volume: 20
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1997.0577

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✦ Synopsis

We prove that the scalar and 2 = 2 matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic structure. Our approach is based on a general graphical method which does not require the modules to be irreducible under the action of Ž . the corresponding Lie super algebra. This method can be generalized to modules of polynomials in an arbitrary number of variables. We given generic examples of partially solvable differential operators which are not Lie algebraic. We show that certain vector-valued modules give rise to new realizations of finite-dimensional Lie superalgebras by first-order differential operators.

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