Character sheaves on symmetric spaces
Author(s)Henderson, Anthony, 1976-
Massachusetts Institute of Technology. Dept. of Mathematics.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.Includes bibliographical references (p. -).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology