The First Eigenvalue of the Dirac Operator on Compact Outer Spin Symmetric Spaces

TL;DR

This paper computes the explicit first eigenvalue of the Dirac operator on outer compact spin symmetric spaces, extending previous work on inner types and providing a complete algebraic characterization.

Contribution

It derives an explicit formula for the first eigenvalue of the Dirac operator on outer symmetric spaces, completing the algebraic analysis for all compact spin symmetric spaces.

Findings

Explicit eigenvalue formula for outer symmetric spaces

Extension of previous results from inner to outer types

Complete algebraic characterization of the first eigenvalue

Abstract

In two previous papers, we started a study of the first eigenvalue of the Dirac operator on compact spin symmetric spaces, providing, for symmetric spaces of "inner" type, a formula giving this first eigenvalue in terms of the algebraic data of the groups involved. We conclude here that study by giving the explicit expression of the first eigenvalue for "outer" compact spin symmetric spaces.