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
DOI:
https://doi.org/10.1090/S0002-9939-98-04506-7
MathSciNet review:
1458255
Full-text PDF
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:
https://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