What question did this study set out to answer?

This research aims to investigate the local Gan-Gross-Prasad conjecture specifically for general spin groups and their representations.

June 20, 2026Open Access

The local Gan-Gross-Prasad conjecture for general spin groups

Key Points

This research aims to investigate the local Gan-Gross-Prasad conjecture specifically for general spin groups and their representations.
Utilizes a structural framework similar to unitary groups.
Addresses both p-adic and Archimedean settings.
Derives a local trace formula linking multiplicity and geometric expansions.
Establishes a multiplicity-one theorem for GGP triples.
Demonstrates connections between spectral expansions and the local trace formula.

Abstract

This dissertation investigates the local Gan-Gross-Prasad conjecture for tempered representations of Gan-Gross-Prasad (GGP) triples associated with general spin groups, extending previous work by Waldspurger for special orthogonal groups and Beuzart-Plessis for unitary groups. We follow the structural framework developed for the unitary case to address both p-adic and Archimedean settings, utilizing the similarities in the root systems and Levi subgroup decompositions of general spin and special orthogonal groups. The primary result establishes a multiplicity-one theorem for the GGP triples. To achieve this, we derive a local trace formula that connects the multiplicity formula with spectral and geometric expansions of a certain distribution.

Mark Helpful

Bookmark

Relay

View Full Paper