The equivariant cohomology of the moduli space of relative quasimaps to the flag variety carries a U(gl_n)-action whose specialized summand is, up to a known category equivalence, a tilting module.
A luna ´ etale slice theorem for algebraic stacks.Annals of mathematics, 191(3):675–738, 2020
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Relative Quasimaps and Tilting Module of $U(\mathfrak{gl}_n)$
The equivariant cohomology of the moduli space of relative quasimaps to the flag variety carries a U(gl_n)-action whose specialized summand is, up to a known category equivalence, a tilting module.