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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.


Fourier transform as a triangular matrix
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by G. Lusztig PDF
Represent. Theory 24 (2020), 470-482 Request permission


Let $V$ be a finite dimensional vector space over the field with two elements with a given nondegenerate symplectic form. Let $[V]$ be the vector space of complex valued functions on $V$, and let $[V]_{\mathbf {Z}}$ be the subgroup of $[V]$ consisting of integer valued functions. We show that there exists a $\mathbf {Z}$-basis of $[V]_{\mathbf {Z}}$ consisting of characteristic functions of certain isotropic subspaces of $V$ and such that the matrix of the Fourier transform from $[V]$ to $[V]$ with respect to this basis is triangular. We show that this is a special case of a result which holds for any two-sided cell in a Weyl group.
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): February 15, 2020
  • Received by editor(s) in revised form: February 22, 2020
  • Published electronically: October 3, 2020
  • Additional Notes: This work was supported by NSF grant DMS-1855773.
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 470-482
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 4156779