Automorphisms of wonderful varieties

TL;DR

This paper investigates the automorphism groups of wonderful G-varieties, providing explicit calculations of their connected automorphism groups and Luna's invariants, thereby advancing understanding of their symmetry structures.

Contribution

It explicitly determines the connected automorphism group of wonderful G-varieties and computes Luna's invariants, offering new insights into their symmetry and classification.

Findings

Connected automorphism groups are explicitly determined.

Luna's invariants of wonderful varieties are calculated.

Results enhance understanding of symmetry in algebraic group actions.

Abstract

Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group of X and we calculate Luna's invariants of X under its action.