Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations
نویسندگان
چکیده
منابع مشابه
On Strong Multiplicity One for Automorphic Representations
We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...
متن کاملREFINEMENT OF STRONG MULTIPLICITY ONE FOR AUTOMORPHIC REPRESENTATIONS OF GL(n)
We state a qualitative form of strong multiplicity one for GL1. We derive refinements of strong multiplicity one for automorphic representations arising from Eisenstein series associated to a Borel subgroup on GL(n), and for the cuspidal representations on GL(n) induced from idele class characters of cyclic extensions of prime degree. These results are in accordance with a conjecture of D. Rama...
متن کاملClassification of multiplicity free symplectic representations
Let G be a connected reductive group acting on a finite dimensional vector space V . Assume that V is equipped with a G-invariant symplectic form. Then the ring O(V ) of polynomial functions becomes a Poisson algebra. The ring O(V ) of invariants is a sub-Poisson algebra. We call V multiplicity free if O(V ) is Poisson commutative, i.e., if {f, g} = 0 for all invariants f and g. Alternatively, ...
متن کاملA Classification of Multiplicity Free Representations
Let G be a connected reductive linear algebraic group over C and let (ρ, V ) be a regular representation of G . There is a locally finite representation (ρ̂,C[V ]) on the affine algebra C[V ] of V defined by ρ̂(g)f(v) = f(g−1v) for f ∈ C[V ] . Since G is reductive, (ρ̂,C[V ]) decomposes as a direct sum of irreducible regular representations of G . The representation (ρ, V ) is said to be multiplic...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2008
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-007-0104-8