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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Representations associated to small nilpotent orbits for complex Spin groups
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by Dan Barbasch and Wan-Yu Tsai PDF
Represent. Theory 22 (2018), 202-222 Request permission

Abstract:

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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Additional Information
  • Dan Barbasch
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850
  • MR Author ID: 30950
  • Email: barbasch@math.cornell.edu
  • 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: wtsai@uottawa.ca, wanyupattsai@gmail.com
  • 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: https://doi.org/10.1090/ert/517
  • MathSciNet review: 3868568