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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.


Representations associated to small nilpotent orbits for complex Spin groups
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by Dan Barbasch and Wan-Yu Tsai
Represent. Theory 22 (2018), 202-222
Published electronically: October 25, 2018


This paper provides a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type $D$. Precisely, let $G_0 =\operatorname {Spin}(2n,\mathbb {C})$ be the Spin complex group as a real group, and let $K\cong G_0$ be the complexification of the maximal compact subgroup of $G_0$. We compute $K$-spectra of the regular functions on some small nilpotent orbits $\mathcal {O}$ transforming according to characters $\psi$ of $C_{ K}(\mathcal {O})$ trivial on the connected component of the identity $C_{ K}(\mathcal {O})^0$. We then match them with the ${K}$-types of the genuine (i.e., representations which do not factor to $\operatorname {SO}(2n,\mathbb {C})$) unipotent representations attached to $\mathcal {O}$.
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Bibliographic Information
  • Dan Barbasch
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850
  • MR Author ID: 30950
  • Email:
  • Wan-Yu Tsai
  • Affiliation: Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan
  • Address at time of publication: Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada
  • MR Author ID: 821037
  • Email:,
  • Received by editor(s): September 5, 2017
  • Received by editor(s) in revised form: April 2, 2018
  • Published electronically: October 25, 2018
  • Additional Notes: The first author was supported in part by NSA Grant H98230-16-1-0006.
  • © Copyright 2018 American Mathematical Society
  • Journal: Represent. Theory 22 (2018), 202-222
  • MSC (2010): Primary 22E46, 22E47
  • DOI:
  • MathSciNet review: 3868568