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Representation Theory

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Compatible intertwiners for representations of finite nilpotent groups

Authors: Masoud Kamgarpour and Teruji Thomas
Journal: Represent. Theory 15 (2011), 407-432
MSC (2010): Primary 20C15
Published electronically: May 16, 2011
MathSciNet review: 2801175
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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

Teruji Thomas
Affiliation: The University of Edinburgh, Edinburgh, United Kingdom EH9 3JZ

Keywords: Orbit method, $p$-groups, neighboring polarizations, Lie rings, intertwiners, Weil representation, determinant, orientation, Maslov index, determinant of abelian groups
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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.