| Abstract |
A (complex) Grassmannian Grk (V) is a homogeneous manifold that parametrizes all k- dimensional linear subspaces of a finite dimensional (complex) vector space V. Using the fact that the orbits of the real form are parametrized by the signature of the Hermitian form restricted to the k-planes in Gr(V), we will take a maximal compact subgroup Ko of Go, its complexification K to establish the celebrated Matsuki-duality in Gr3(C). In this setup, Matsuki-duality is a pairing between the finitely many Go-orbits and K-orbits on Gr3(C). In the following talk, we'll establish the Matsuki-duality in concrete terms by characterizing the existence of the Matsuki-dual Ko-orbit in the case of Gr3(C). At the end, we will have a glance at different cases with regards to different signatures
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