Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.
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Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\text{SL}_2$
Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.