Restriction of a character sheaf to conjugacy classes
Name
Lusztig_Restriction of a character.pdf
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360.36 KB
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4e0fbf93f0798c1ebc4afe0b0286ab3c
Author(s)
Lusztig, George
Date Issued
2015
Journal
Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie
Publisher
Societatea de Ştiinţe Matematice din România
Citation
Lusztig, G. “Restriction of a character sheaf to conjugacy class.” Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie 106.3 (2015): 287–309.
Version
Original manuscript
Abstract
Let A be a character sheaf on a connected reductive group G over an algebraically closed field. Assuming that the characteristic is not bad we show that for certain conjugacy classes D in G, the restriction of A to D is a local system up to shift. We also give a parametrization of unipotent cuspidal character sheaves of G in terms of restriction to conjugacy classes. Without restriction on characteristic we define canonical bijections from the set of unipotent representations of the corresponding split group over a finite field to a set combinatorially defined in terms of the Weyl group.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
http://ssmr.ro/bulletin/volumes/58-3/node8.html
