8 On a p - adic extension of the Jacquet - Langlands correspondence to weight 1

Deligne-lusztig Constructions for Division Algebras and the Local Langlands Correspondence

Let K be a local non-Archimedean field of positive characteristic and let L be the degree-n unramified extension of K. Let θ be a smooth character of L× such that for each nontrivial γ ∈ Gal(L/K), θ and θ/θ have the same level. Via the local Langlands and Jacquet-Langlands correspondences, θ corresponds to an irreducible representation ρθ of D×, where D is the central division algebra over K wi...

The Jacquet-Langlands correspondence via `-adic uniformization

ON REPRESENTATION THEORY OF GL(n) OVER p-ADIC DIVISION ALGEBRA AND UNITARITY IN JACQUET-LANGLANDS CORRESPONDENCE

Let F be a p-adic field of characteristic 0, and let A be an F -central division algebra of dimension dA over F . In the paper we first develop the representation theory of GL(m,A), assuming that holds the conjecture which claims that unitary parabolic induction is irreducible for GL(m,A)’s. Among others, we obtain the formula for characters of irreducible unitary representations of GL(m,A) in ...

WEAK EXPLICIT MATCHING FOR LEVEL ZERO DISCRETE SERIES OF UNIT GROUPS OF p-ADIC SIMPLE ALGEBRAS

Let F be a p-adic local eld and let A i be the unit group of a central simple F-algebra A i of reduced degree n > 1 (i = 1; 2). Let R 2 (A i) denote the set of irreducible discrete series representations of A i. The \Abstract Matching Theorem" asserts the existence of a bijection, the \Jacquet-Langlands" map,A 2) which, up to known sign, preserves character values for regular elliptic elements....

On Classification of Some Classes of Irreducible Representations of Classical Groups

Introduction 2 1. Harmonic analysis and unitary duals 2 2. Non-discrete locally compact fields, classical groups, reductive groups 4 3. K0-finite vectors 7 4. Smooth representations 8 5. Parabolically induced representations 9 6. Jacquet modules 12 7. Filtrations of Jacquet modules 14 8. Square integrable and tempered representations 15 9. Langlands classification 16 10. Geometric lemma and alg...