Decomposition of splitting invariants in split real groups

TL;DR

This paper analyzes the splitting invariants of maximal tori in split real groups, providing a decomposition theorem that simplifies their computation and comparison across different tori.

Contribution

It introduces a decomposition theorem for splitting invariants in split real groups, enabling easier calculation and comparison of these invariants.

Findings

Decomposition of splitting invariants into products for simple tori

Reduction formula for comparing invariants across tori

Facilitates calculations in endoscopic transfer factors

Abstract

To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of their endoscopic transfer factors. We study this invariant in the case of a split real group and prove a decomposition theorem which expresses this invariant for a general torus as a product of the corresponding invariants for simple tori. We also show how this reduction formula allows for the comparison of splitting invariants between different tori in the given real group.