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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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Compatible intertwiners for representations of finite nilpotent groups
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by Masoud Kamgarpour and Teruji Thomas PDF
Represent. Theory 15 (2011), 407-432 Request permission

Abstract:

We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized by an additional choice of polarization. Our construction is motivated by the theory of the linearized Weil representation of the symplectic group. In particular, we provide generalizations of the Maslov index and the determinant functor to the context of finite abelian groups.
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Additional Information
  • Masoud Kamgarpour
  • Affiliation: The University of British Columbia, Vancouver, Canada V6T 1Z2
  • Email: masoud@math.ubc.ca
  • Teruji Thomas
  • Affiliation: The University of Edinburgh, Edinburgh, United Kingdom EH9 3JZ
  • Email: t.thomas@ed.ac.uk
  • Received by editor(s): October 29, 2009
  • Received by editor(s) in revised form: August 16, 2010
  • Published electronically: May 16, 2011
  • Additional Notes: The first author was supported by NSERC PDF grant. The second author was supported by a JRF at Merton College, Oxford and a Seggie Brown Fellowship at Edinburgh.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 407-432
  • MSC (2010): Primary 20C15
  • DOI: https://doi.org/10.1090/S1088-4165-2011-00395-2
  • MathSciNet review: 2801175