K-orbit closures and Barbasch-Evens-Magyar varieties

We define the Barbasch-Evens-Magyar variety. We show it is isomorphic to the smooth variety defined in [D. Barbasch-S. Evens u002794] that maps finite-to-one to a symmetric orbit closure, thereby giving a resolution of singularities in certain cases. Our definition parallels [P. Magyar u002798]u0027s construction of the Bott-Samelson variety [H. C. Hansen u002773, M. Demazure u002774]. 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. We then prove that the moment polytope is expressed in terms of the moment polytope of a Bott-Samelson variety.