Black Holes and Groups of Type E7

TL;DR

This paper explores the connection between extremal black holes in supersymmetric gravity theories and the mathematical structure of groups of type E7, highlighting their role in duality symmetries and geometric frameworks.

Contribution

It provides new insights into the relation between black hole solutions and E7 groups, including a covariant approach and links to special Kaehler geometry.

Findings

Identifies the role of E7 groups in black hole duality symmetries

Develops a covariant stratification approach for symplectic representations

Connects special Kaehler geometry with generalized E7 groups

Abstract

We report some results on the relation between extremal black holes in locally supersymmetric theories of gravity and groups of type E7, appearing as generalized electric-magnetic duality symmetries in such theories. Some basics on the covariant approach to the stratification of the relevant symplectic representation are reviewed, along with a connection between special Kaehler geometry and a "generalization" of groups of type E7.