Character sheaves on symmetric spaces
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. === Includes bibliographical references (p. [79]-[80]). === 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...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | English |
| Published: |
Massachusetts Institute of Technology
2005
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/8638 |
| Summary: | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. === Includes bibliographical references (p. [79]-[80]). === 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. === by Anthony Henderson. === Ph.D. |
|---|