Classification of Equivariant Legendrian Embeddings of Rational Homogeneous Spaces into Nilpotent Orbits

TL;DR

This paper classifies equivariant Legendrian embeddings of rational homogeneous spaces into nilpotent orbits, revealing the structure of Legendrian subvarieties with symmetry properties in complex contact geometry.

Contribution

It provides a comprehensive classification of equivariant Legendrian embeddings of rational homogeneous spaces into nilpotent orbits, advancing understanding of their geometric and algebraic properties.

Findings

Classification of projective Legendrian subvarieties for each nilpotent orbit

Explicit description of equivariant Legendrian embeddings of rational homogeneous spaces

Insights into the structure of Legendrian subvarieties in complex contact geometry

Abstract

For a complex semi-simple Lie algebra, every nilpotent orbit in its projectivization comes with a complex contact structure. For each nilpotent orbit, we classify projective Legendrian subvarieties that are homogeneous under the actions of their stabilizers in the adjoint group. In particular, we present a classification of equivariant Legendrian embeddings of rational homogeneous spaces into adjoint varieties.