A `relative' local Langlands correspondence

2015/12/14 by Dipendra Prasad, Prasad, Dipendra · 6 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1512.04347

Abstract

For E/F quadratic extension of local fields and G a reductive algebraic group over F, the paper formulates a conjecture classifying irreducible admissible representations of G(E) which carry a G(F) invariant linear form, and the dimension of the space of these invariant forms, in terms of the Langlands parameter of the representation. The paper studies parameter spaces of Langlands parameters, and morphisms between them associated to morphisms of L-groups. The conjectural answer to the question on the space of G(F)-invariant linear forms is in terms of fibers of a particular finite map between parameter spaces.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Cited by

• Distinguished representations for SL(n)
• Supercuspidal representations of GL_n(F) distinguished by an orthogonal involution
• Multiplicities and Plancherel formula for the space of nondegenerate\n Hermitian matrices
• Generalizing the MVW involution, and the contragredient
• Distinguished regular supercuspidal representations
• Theta lifts and distinction for regular supercuspidal representations

Related

• Admissible embedding of L-groups and essentially tame local Langlands correspondence
• Representations of reductive groups over local fields
• On the local Langlands correspondence
• Langlands Classification for L-Parameters
• Lowest K-types in the local Langlands correspondence