Modular representations of GL(3, F-p), symmetric squares, and mod-p cohomology of GL(3, Z)

Authors
Ash, A Tiep, PH
Citation
A. Ash et Ph. Tiep, Modular representations of GL(3, F-p), symmetric squares, and mod-p cohomology of GL(3, Z), J ALGEBRA, 222(2), 1999, pp. 376-399
Citations number
24
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF ALGEBRA
ISSN journal
00218693 → ACNP
Volume
222
Issue
2
Year of publication
1999
Pages
376 - 399
Database
ISI
SICI code
0021-8693(199912)222:2<376:MROGFS>2.0.ZU;2-H
Abstract
We prove certain cases of nonabelian reciprocity between mod p Galois repre sentations and Hecke eigenclasses in the mod p cohomology of GL(3, Z), usin g the symmetric square liftings from GL(2) and congruences on Hecke eigenva lues. We need to develop some modular representation theory for GL(3, Zip). In some cases we also need to invoke certain computer calculations to fini sh the proof. (C) 1999 Academic Press.