An orthogonal family of polynomials

on the generalized unit disk

and ladder representations of

Author:
John D. Lorch

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3755-3762

MSC (1991):
Primary 22E45, 22E70; Secondary 32L25, 32M15, 58G05, 81R05, 81R25

MathSciNet review:
1458255

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Abstract | References | Similar Articles | Additional Information

Abstract: Inner product structures are given for realizations of the positive spin ladder representations over the generalized unit disk . This is accomplished by combining previous results of the author with the construction of a family of holomorphic polynomials on . These polynomials, which play a crucial role in the present work, are shown to be orthogonal with respect to Lebesgue measure, and their norms are computed. The orthogonal family is then used to invert a certain integral transform, giving the desired inner product structures.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04506-7

Keywords:
Ladder representations,
unitary structures,
Penrose transform,
generalized unit disk

Received by editor(s):
January 2, 1997

Received by editor(s) in revised form:
April 28, 1997

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1998
American Mathematical Society