Modular Representations of GL(3, Fp), Symmetric Squares, and Mod-p Cohomology of GL(3, Z)

✍ Scribed by Avner Ash; Pham Huu Tiep

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 190 KB
• Volume: 222
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.7988

✦ Synopsis

We prove certain cases of nonabelian reciprocity between mod p Galois representations and Hecke eigenclasses in the mod p cohomology of GL 3 , using the symmetric square liftings from GL 2 and congruences on Hecke eigenvalues. We need to develop some modular representation theory for GL 3 /p . In some cases we also need to invoke certain computer calculations to finish the proof.