Fixed points and components of equivalued affine Springer fibers

TL;DR

This paper studies the structure of affine Springer fibers for semisimple groups, focusing on their components and fixed points, especially in Type A, to deepen understanding of their geometric and combinatorial properties.

Contribution

It revisits the component description of affine Springer fibers for regular semisimple elements and computes fixed points in Type A, providing new insights into their structure.

Findings

Revised description of components of affine Springer fibers for regular semisimple elements.

Explicit computation of fixed points in Type A affine Springer fibers.

Enhanced understanding of the geometric structure of affine Springer fibers.

Abstract

For G a semisimple algebraic group, we revisit the description of the components of the affne Springer fiber given by ts, with s a regular semisimple element. We then compute the fixed points of each component of a particular affne Springer fiber for Type A