TY - JOUR
T1 - Modular representations of gl2 of a local-field
T2 - The ordinary, unramified case
AU - Barthel, L.
AU - Livné, R.
PY - 1995/11
Y1 - 1995/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0001785218&partnerID=8YFLogxK
U2 - 10.1006/jnth.1995.1124
DO - 10.1006/jnth.1995.1124
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0001785218
SN - 0022-314X
VL - 55
SP - 1
EP - 27
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -