Periods and harmonic analysis on spherical varieties / Yiannis Sakellaridis, Akshay Venkatesh.

Format:

Book

Author/Creator:

Sakellaridis, Yiannis, author.

Venkatesh, Akshay, 1981- author.

Series:

Astérisque ; 396.

Astérisque, 0303-1179 ; 396

Language:

English

French

Subjects (All):

Harmonic analysis.

Automorphic forms.

Physical Description:

viii, 360 pages ; 24 cm.

Contained In:

Astérisque no:396

Place of Publication:

Paris : Société mathématique de France, 2017.

Language Note:

In English with abstracts in English and French.

Summary:

This volume elaborates the idea that harmonic analysis on a spherical variety X is intimately connected to the Langlands program. In the local setting, the key conjecture is that the spectral decomposition of L^2(X) is controlled by a dual group attached to X. Guided by this, the authors develop a Plancherel formula for L^2(X), formulated in terms of simpler spherical varieties which model the geometry of X at infinity. This local study is then related to global conjectures--namely, conjectures about period integrals of automorphic forms over spherical subgroups.--Publisher's website.

Contents:

Part 1. The dual group of a spherical variety

Review of spherical varieties

Proofs of the results on the dual group

Part II. Local theory and the Ichino-Ikeda conjecture

Geometry over a local field

Asymptotics

Strongly tempered varieties

Part III. Spectral decomposition and scattering theory

Results

Two toy models: the global picture and semi-infinite matrices

The discrete spectrum

Preliminaries to the Bernsteins morphisms: "linear algebra"

The Bernstein morphisms

Preliminaries to scattering(I): direct integrals and norms

Preliminaries to scattering (II): consequences of the conjecture on discrete series

Scattering theory

Explicit Plancherel formula

Part IV: Conjectures

The local X-distinguished spectrum

Speculation on a global period formula

Examples

A. Prime rank one spherical varieties.

Notes:

Includes bibliographical references (pages 353-360).

ISBN:

9782856298718

2856298710

OCLC:

1027787539