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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Analytic families of eigenfunctions on a reductive symmetric space
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by E. P. van den Ban and H. Schlichtkrull
Represent. Theory 5 (2001), 615-712
Published electronically: December 12, 2001


Let $X=G/H$ be a reductive symmetric space, and let $\mathbb D(X)$ denote the algebra of $G$-invariant differential operators on $X$. The asymptotic behavior of certain families $f_\lambda$ of generalized eigenfunctions for $\mathbb D(X)$ is studied. The family parameter $\lambda$ is a complex character on the split component of a parabolic subgroup. It is shown that the family is uniquely determined by the coefficient of a particular exponent in the expansion. This property is used to obtain a method by means of which linear relations among partial Eisenstein integrals can be deduced from similar relations on parabolic subgroups. In the special case of a semisimple Lie group considered as a symmetric space, this result is closely related to a lifting principle introduced by Casselman. The induction of relations will be applied in forthcoming work on the Plancherel and the Paley-Wiener theorem.
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Bibliographic Information
  • E. P. van den Ban
  • Affiliation: Mathematisch Institut, Universiteit Utrecht, PO Box 80 010, 3508 TA Utrecht, The Netherlands
  • MR Author ID: 30285
  • Email:
  • H. Schlichtkrull
  • Affiliation: Matematisk Institut, Københavns Universitet, Universitetsparken 5, 2100 København Ø, Denmark
  • MR Author ID: 156155
  • ORCID: 0000-0002-4681-3563
  • Email:
  • Received by editor(s): February 20, 2001
  • Received by editor(s) in revised form: September 6, 2001
  • Published electronically: December 12, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 615-712
  • MSC (2000): Primary 22E30, 22E45
  • DOI:
  • MathSciNet review: 1870604