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
,
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 express the
moment polytope in terms of the moment polytope of a Bott–Samelson
variety.
Keywords
flag variety, $\sf{K}$-orbit, Barbasch–Evens–Magyar
variety, moment polytope, clans
