Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An orthogonal family of polynomials
on the generalized unit disk
and ladder representations of $U(p,q)$


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
Full-text PDF Free Access

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 ${\bf D}_{p,q} =U(p,q)/K$. This is accomplished by combining previous results of the author with the construction of a family of holomorphic polynomials on ${\bf D}_{p,q}$. 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22E45, 22E70, 32L25, 32M15, 58G05, 81R05, 81R25

Retrieve articles in all journals with MSC (1991): 22E45, 22E70, 32L25, 32M15, 58G05, 81R05, 81R25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04506-7
PII: S 0002-9939(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