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5. Affine Springer fibers and braid varieties


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      Problem 5.1.

      What relationship is there between braid varieties and affine Springer fibers in the affine Grassmannian?

        •     Let $GCD(k,n)=1$, let $U(k,n)$ be the quotient of the big positroid cell in $G(k,n)$ by $(\mathbb{C}^*)^n$. It has all $H^*$ in even degree.

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          Problem 5.2.

          Why does there exist an affine springer fiber with the same betti numbers and a cell decomposition? Do the rings match?


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              Problem 5.3.

              Is there a similar story for other cluster varieties or braid varieties?


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                  Problem 5.4.

                  What do the cluster structures correspond to on the springer fiber?

                      Cite this as: AimPL: Cluster algebras and braid varieties, available at http://aimpl.org/clusterbraid.