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.
Finite difference quantum toda lattice via equivariant k-theory.Transformation Groups, 10:363–386, 2005
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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.