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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.


On certain small representations of indefinite orthogonal groups
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by Chen-bo Zhu and Jing-Song Huang
Represent. Theory 1 (1997), 190-206
Published electronically: July 17, 1997


For any $n\in \mathbb {N}$ such that $2n\leq \min (p,q)$, we construct a representation $\pi _{n}$ of $O(p,q)$ with $p+q$ even as the kernel of a commuting set of $\frac {n(n+1)}{2}$ number of $O(p,q)$-invariant differential operators in the space of $C^{\infty }$ functions on an isotropic cone with a distinguished $GL_{n}(\mathbb {R})$-homogeneity degree. By identifying $\pi _{n}$ with a certain representation constructed via the formalism of the theta correspondence, we show (except when $p=q=2n$) that the space of $K$-finite vectors of $\pi _{n}$ is the $(\mathfrak {g},K)$-module of an irreducible unitary representation of $O(p,q)$ with Gelfand-Kirillov dimension $n(p+q-2n-1)$. Our construction generalizes the work of Binegar and Zierau (Unitarization of a singular representation of $SO_{e}(p,q)$, Commun. Math. Phys. 138 (1991), 245โ€“258) for $n=1$.
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Bibliographic Information
  • Chen-bo Zhu
  • Affiliation: Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260
  • MR Author ID: 305157
  • ORCID: 0000-0003-3819-1458
  • Email:
  • Jing-Song Huang
  • Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
  • MR Author ID: 304754
  • Email:
  • Received by editor(s): September 4, 1996
  • Received by editor(s) in revised form: January 9, 1997
  • Published electronically: July 17, 1997
  • © Copyright 1997 American Mathematical Society
  • Journal: Represent. Theory 1 (1997), 190-206
  • MSC (1991): Primary 22E45, 22E46
  • DOI:
  • MathSciNet review: 1457244