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), 37553762
MSC (1991):
Primary 22E45, 22E70; Secondary 32L25, 32M15, 58G05, 81R05, 81R25
MathSciNet review:
1458255
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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/S0002993998045067
PII:
S 00029939(98)045067
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
