Flag varieties as equivariant compactifications of G_a^n

TL;DR

This paper classifies flag varieties G/P that can be compactified with an open orbit under an action of the commutative unipotent group G_a^n, revealing new geometric structures.

Contribution

It provides a complete classification of flag varieties admitting G_a^n-actions with open orbits, connecting algebraic group actions with geometric compactifications.

Findings

Identifies all flag varieties with G_a^n-action and open orbit

Establishes criteria for equivariant compactifications of G_a^n

Links group actions to geometric structures of flag varieties

Abstract

Let G be a semisimple affine algebraic group and P a parabolic subgroup of G. We classify all flag varieties G/P which admit an action of the commutative unipotent group G_a^n with an open orbit.