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AN INTERTWINING OPERATOR FOR THE GROUP B 2

Published online by Cambridge University Press:  09 August 2007

CHARLES F. DUNKL
CHARLES F. DUNKL*
Affiliation:
Department of Mathematics, PO Box 400137, University of Virginia, Charlottesville, VA 22904-4137 e-mail: cfd5z@virginia.edu URL: http://www.people.virginia.edu/~cfd5z/
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Abstract

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There is a commutative algebra of differential-difference operators, acting on polynomials on $\mathbb{R}^{2}$, associated with the reflection group B 2. This paper presents an integral transform which intertwines this algebra, allowing one free parameter, with the algebra of partial derivatives. The method of proof depends on properties of a certain class of balanced terminating hypergeometric series of 4 F 3-type. These properties are in the form of recurrence and contiguity relations and are proved herein.

Keywords

Primary 33C8033C20Secondary 33C7043A80

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 291 - 319
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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