Naive boundary strata and nilpotent orbits

TL;DR

This paper investigates specific real Lie-group orbits in Mumford-Tate domains, confirming a prior prediction and identifying which orbits contain limit points of period maps, with detailed examples for certain groups.

Contribution

It verifies a prediction about real Lie-group orbits in Mumford-Tate domains and characterizes limit points of period maps within these orbits.

Findings

Confirmed the prediction about orbit structure in Mumford-Tate domains.

Identified which orbits contain limit points of period maps.

Provided explicit examples for groups SU(2,1), Sp_4, and G_2.

Abstract

We study certain real Lie-group orbits in the compact duals of Mumford-Tate domains, verifying a prediction made in [Green, Griffiths, Kerr; Mumford-Tate domains: their geometry and arithmetic] and determining which orbits contain a limit point of some period map. A variety of examples are worked out for the groups SU(2,1), Sp_4, and G_2.