On the Fixed Points of a Regular Unipotent Element

TL;DR

This paper investigates the fixed point varieties of regular unipotent elements on wonderful completions, revealing that for quotients by symmetric Levi subgroups, these fixed points are $SL_2$-regular, contributing to algebraic group theory.

Contribution

It demonstrates that fixed point varieties are $SL_2$-regular in the case of wonderful completions of quotients by symmetric Levi subgroups, a new insight in the structure of these varieties.

Findings

Fixed point varieties are $SL_2$-regular for certain quotients.

The study advances understanding of unipotent elements in algebraic groups.

Provides new structural results in the theory of wonderful completions.

Abstract

The fixed point variety of a regular unipotent element on a wonderful completion is investigated. For the wonderful completion of the quotient by a symmetric Levi subgroup, it is shown that the fixed point variety is $SL_2$-regular.