A note on period domains of Hodge structures

TL;DR

This paper explores the structure of period domains of complex Hodge structures, focusing on their properties from a representation theory perspective, including automorphic cohomology and complex structures on symmetric spaces.

Contribution

It introduces the automorphic cohomology of period domains and examines their complex structures, offering new insights from a representation theory viewpoint.

Findings

Characterization of period domains as symmetric spaces

Introduction of automorphic cohomology for period domains

Analysis of complex structures on symmetric spaces

Abstract

We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric spaces.