Character sheaves on symmetric spaces
Name
49612548-MIT.pdf
Description
Full printable version
Size
5.83 MB
Format
Adobe PDF
Checksum (MD5)
2365ba513456ca114cd40e422fd16b6e
Author(s)
Henderson, Anthony, 1976-
Advisor(s)
George Lusztig.
Date Issued
2001
Publisher
Massachusetts Institute of Technology
Abstract
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]).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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