FOURIER TRANSFORM AS A TRIANGULAR MATRIX
Name
S1088-4165-2020-00551-5.pdf
Description
Published version
Size
187.95 KB
Format
Unknown
Checksum (MD5)
a800a721e6df38ae0cf10d355e4c3a5e
Author(s)
Lusztig, George
Date Issued
October 3, 2020
Journal
Representation Theory
Publisher
American Mathematical Society (AMS)
Version
Final published version
Abstract
©2020 American Mathematical Society abstract. 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]z be the subgroup of [V] consisting of integer valued functions. We show that there exists a Z-basis of [V]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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/ert/551
