6 problems

Let $ctilde{\operatorname{Sp}}_gamma$ be the relevant enhanced affine Springer fiber, with Springer action on its homology. Tsai's regular-representation conjecture. The Springer a…

Let $\{\lambda_i\}$ be a nested sequence of Young diagrams such that … with $|\lambda_i|=i$. Let $\tau_{k+1}=(k+1,k,\ldots,1)$, and define the $k$-stable shape of $\{\lambda_i\}$ b…

Let $\{\lambda_n\}$ be a nested sequence of Young diagrams with $|\lambda_n|=n$, and let $p_k(n)$ denote the eventual dimension polynomial for the degree-$k$ part of the Springer r…

Let $\lambda$ be a Young diagram and let $\mathcal{B}(\lambda)$ denote the GP-basis of the Springer quotient $R_n/I_\lambda$. A monomial type records the exponents of a monomial, a…

Let $\mathcal{B}(\lambda)$ be the GP-basis associated to a Young diagram $\lambda$, and let a monomial type mean the multiset of exponents appearing in a monomial. Order monomials…

Kraft's conjecture. The action of $W$ on $H^*(\mathcal B_x)$ is equivalent to the action of $W$ on $A(\mathfrak{t}\cap C_y)$.