Noncommutative resolutions of affine Schubert varieties in type A and canonical bases (opens in new tab)

Given a resolution $\widetilde{\mathrm{Gr}}^{\underline{\lambda}} \rightarrow \overline{\mathrm{Gr}}^\lambda$ of an affine Schubert variety for $GL_n$, we define its noncommutative version -- a sheaf of algebras on $\overline{\mathrm{Gr}}^\lambda$, derived equivalent to $\widetilde{\mathrm{Gr}}^{\underline{\lambda}}$ as well as its Steinberg versions in both zero and positive characteristics. This, in particular, allows us to define the perver...