Modular representations of gl2 of a local-field: The ordinary, unramified case

L. Barthel, R. Livné

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Abstract

Let F be a local field of residue characteristic p, and let E be an algebraically closed field of characteristic p. We prove that unramified irreducible representations of PGL2(F) on E- vector spaces admit eigenvectors for an appropriate Hecke operator T. We classify them by the eigenvalue λ of T to one dimensional (λ = ± 1), principal series (λ ≠ 0, ± 1) or supersingular (λ = 0). Any λ can appear, and for λ ≠ 0 we prove uniqueness.

Original languageAmerican English
Pages (from-to)1-27
Number of pages27
JournalJournal of Number Theory
Volume55
Issue number1
DOIs
StatePublished - Nov 1995

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