Some consequences of Arthur's conjectures for special orthogonal even groups
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Octavio Paniagua-Taboada
Abstract
In this paper we construct explicitly through Eisenstein series, a square integrable residual automorphic representation of the special orthogonal group SO2n. We show that this representation comes from an elliptic Arthur parameter and it appears in the space L2(SO2n()\SO2n()) with multiplicity one. Next, we consider parameters whose Hecke matrices, at the unramified places, have eigenvalues bigger in absolute value than those of the parameter constructed before. The main result is that these parameters cannot be cuspidal. We establish bounds for the eigenvalues of Hecke operators, as consequences of Arthur's conjectures for SO2n. Next, we calculate the character and the twisted characters for the representations that we considered and we prove an identity of traces. Finally, we find the composition of the global and local Arthur's packets associated to our parameter . All the results in this paper are true if we replace by any number field F.
Walter de Gruyter Berlin New York 2011
Articles in the same Issue
- On the cyclotomic main conjecture for the prime 2
- Some consequences of Arthur's conjectures for special orthogonal even groups
- Cartier modules: Finiteness results
- RiemannHilbert problem for Hurwitz Frobenius manifolds: Regular singularities
- Prime factors of dynamical sequences
- Enriques manifolds
- Volume versus rank of lattices
Articles in the same Issue
- On the cyclotomic main conjecture for the prime 2
- Some consequences of Arthur's conjectures for special orthogonal even groups
- Cartier modules: Finiteness results
- RiemannHilbert problem for Hurwitz Frobenius manifolds: Regular singularities
- Prime factors of dynamical sequences
- Enriques manifolds
- Volume versus rank of lattices
