K-ORBIT CLOSURES AND BARBASCH–EVENS–MAGYAR VARIETIES

We define the Barbasch–Evens–Magyar varieties. We show they are isomorphic to the smooth varieties defined in [D. Barbasch and S. Evens 1994] that map generically finitely to symmetric orbit closures, thereby giving resolutions of singularities in certain cases. Our definition parallels P. Magyar’s [1998] construction of the Bott–Samelson varieties [H. C. Hansen 1973; M. Demazure 1974]. From this alternative viewpoint, one deduces a graphical description in type A, stratification into closed subvarieties of the same kind, and determination of the torus-fixed points. Moreover, we explain how these manifolds inherit a natural symplectic structure with Hamiltonian torus action.