TY - JOUR

T1 - Experimental indications of three-dimensional Galois representations from the cohomology of SL(3, Z)

AU - Ash, Avner

AU - McConnell, Mark

PY - 1992

Y1 - 1992

N2 - Conjecturally, any "algebraic" automorphic representation on GL(n)should have an n-dimensional Galois representation attached. Many examples of algebraic automorphic representations come from the cohomology over Cof congruence subgroups of GL(n;Z). On the other hand, the first author has conjectured that for any Hecke eigenclass in the mod pcohomology of a congruence subgroup of GL(n;Z)there should be an attached n-dimensional Galois representation. By computer, we found Hecke eigenclasses in the mod pcohomology of certain congruence subgroups of SL(3;Z). In a range of examples, we then found a Galois representation (uniquely determined up to isomorphism by our data) that seemed to be attached to the Hecke eigenclass.

AB - Conjecturally, any "algebraic" automorphic representation on GL(n)should have an n-dimensional Galois representation attached. Many examples of algebraic automorphic representations come from the cohomology over Cof congruence subgroups of GL(n;Z). On the other hand, the first author has conjectured that for any Hecke eigenclass in the mod pcohomology of a congruence subgroup of GL(n;Z)there should be an attached n-dimensional Galois representation. By computer, we found Hecke eigenclasses in the mod pcohomology of certain congruence subgroups of SL(3;Z). In a range of examples, we then found a Galois representation (uniquely determined up to isomorphism by our data) that seemed to be attached to the Hecke eigenclass.

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U2 - 10.1080/10586458.1992.10504259

DO - 10.1080/10586458.1992.10504259

M3 - Article

AN - SCOPUS:0000159591

SN - 1058-6458

VL - 1

SP - 209

EP - 223

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 3

ER -