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Some consequences of Arthur's conjectures for special orthogonal even groups
- Source :
- Journal für die reine und angewandte Mathematik (Crelles Journal). 2011:37-84
- Publication Year :
- 2011
- Publisher :
- Walter de Gruyter GmbH, 2011.
-
Abstract
- In this paper we construct explicitly a square integrable residual automorphic representation of the special orthogonal group $SO_{2n}$, through Eisenstein series. We show that this representation comes from an elliptic Arthur parameter $\psi$ and appears in the space $L^2(SO_{2n}(\mathbb{Q})\backslash SO_{2n}(\mathbb{A}_{\mathbb{Q}}))$ 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 $SO_{2n}$. Next, we calculate the character and the twisted characters for the representations that we constructed. Finally, we find the composition of the global and local Arthur's packets associated to our parameter $\psi$. All the results in this paper are true if we replace $\mathbb{Q}$ by any number field $F$.<br />Comment: 39 pages
- Subjects :
- Mathematics - Number Theory
Applied Mathematics
General Mathematics
Absolute value (algebra)
Algebraic number field
Space (mathematics)
Combinatorics
symbols.namesake
Character (mathematics)
Square-integrable function
Mathematics::Quantum Algebra
Eisenstein series
FOS: Mathematics
symbols
22E50, 22E55, 11F25, 11F70
Orthogonal group
Number Theory (math.NT)
Representation Theory (math.RT)
Mathematics::Representation Theory
Mathematics - Representation Theory
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 14355345 and 00754102
- Volume :
- 2011
- Database :
- OpenAIRE
- Journal :
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Accession number :
- edsair.doi.dedup.....0590d78284662bd33e9a431e991effb7