Lie algebras a with complex underlying vector space V are
 studied that are automorphic respect to given linear
 dynamical system on , i.e., 1-parameter subgroup Gt ⊂
 Aut(a) ⊂ GL(V ). Each algebra imparts a
 algebraic structure the of trajectories of
 group Gt. The basics general automorphic
 described in terms eigenspace
 decomposition operatorM ∈ der(a) det...

We have determined composition series of a class induced representations appearing in Mœglin–Tadić classification discrete series. The result is further used to determine the certain from Langlands quotients. This should provide more information on decomposing standard as well Jacquet modules series, which has applications automorphic forms.

Certain nontempered liftings from PGL (2) × PGL (2) to PGSp (4) are constructed using the theory of (local and global) theta lifts. The resulting representations on PGSp (4) are the SaitoKurokawa representations. The lifting is shown to be functorial under certain reasonable assumptions on the local Langlands correspondence for PGSp (4). Introduction. The classical Saito-Kurokawa lifting associ...

Two of the primary methods of constructing automorphic forms are the Langlands program and Howe's theory of dual pairs. The Langlands program concerns a reductive linear group G deened over a number eld. Associated to G is its dual group L G. The con-jectural principle of functoriality says that a homomorphism L H ! L G should provide a \transfer" of automorphic representations from H to those ...

By applying the residue method for period integrals, we prove identities between integrals on cuspidal automorphic representations and residual seven spherical varieties. Combining this with Langlands–Shahidi theory residues of Eisenstein series, each case, some relations certain L-functions. In cases, also study local multiplicity

Let π be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GLn(AF ), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic Galois representations associated to π are irreducible, and for all but finitely many primes l, the mod l Galois representations associated to π are also irreducible. We also show that the Lie algebras...

Abstract In this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems representations, and apply it deduce results for both automorphic positive characteristic settings. the abstract case, an result Lie-irreducible from which admitting what call decomposition. case geometric Galois representations arising certain classes forms, existence Fr...