Extending local representations to global representations

Irreducibility Criteria for Local and Global Representations

It is proved that certain types of modular cusp forms generate irreducible automorphic representations of the underlying algebraic group. Analogous Archimedean and non-Archimedean local statements are also given. Introduction One of the motivations for this paper was to show that full level cuspidal Siegel eigenforms generate irreducible, automorphic representations of the adelic symplectic sim...

Lifting Global Representations with Local Properties

Let k be a global field, with Galois group Gk and Weil group Wk relative to a choice of separable closure ks/k. Let Γ be either Gk or Wk, and H a linear algebraic group over F = C or Qp with p 6= char(k). Let ρ : Γ→ H(F ) be a (continuous) representation, always understood to be ramified at only finitely many places (as is automatic for commutative H, but not for H = GL2 with k = Q and F = Qp, ...

Towards Extending Domain Representations

Local-to-global extensions of representations of fundamental groups

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Distinguished positive regular representations

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...