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

Avner Ash, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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

Original languageEnglish (US)
Pages (from-to)376-399
Number of pages24
JournalJournal of Algebra
Issue number2
StatePublished - Dec 15 1999


  • Galois representations
  • Mod-p cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory


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