Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\text{SL}_2$

TL;DR

This paper analyzes how Schubert cells in the affine flag variety of SL_2 decompose into orbits under specific subgroups of the Iwahori group, revealing detailed subgroup orbit structures.

Contribution

It provides a detailed description of the orbit decomposition of Schubert cells under subgroups of the Iwahori group in the affine flag variety of SL_2.

Findings

Decomposition of Schubert cells into orbits under subgroups of codimension one to four.

Explicit descriptions of orbit structures for each subgroup.

Enhanced understanding of subgroup actions in affine flag varieties.

Abstract

We describe how each finite dimensional Schubert cell in the affine flag variety of $\text{SL}_2$ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group.