Character sheaves on symmetric spaces
Author(s)
Henderson, Anthony, 1976-
DownloadFull printable version (5.829Mb)
Other Contributors
Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
George Lusztig.
Terms of use
Metadata
Show full item recordAbstract
Inspired by the work of Lusztig, we apply the theory of character sheaves on a symmetric space (h la Ginzburg and Grojnowski) to the problem of determining the spherical functions (averages of the irreducible characters) of the associated symmetric space over a finite field. A crucial result about the filtration of character sheaves by cells enables us to compute the spherical functions explicitly in the cases GLn((Fq2)/GLn(]Fq) and GL2n(1Fq)/Sp2n((Fq), as well as other closely related examples. We include partial results about the symmetric space GLn/(GLm x GLn-m), to illustrate some of the obstacles to further generalization.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. Includes bibliographical references (p. [79]-[80]).
Date issued
2001Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.