Full Set of Invariants Characterizing Sp(n)-Orbits in Real Grassmannians GR(k, 4n)

Explore a comprehensive lecture on the determination of invariants for Sp(n)-orbits in real Grassmannians GR(k, 4n). Delve into the mathematical foundations of Hermitian quaternionic structures, hypercomplex structures, and isoclinic subspaces. Learn about the canonical I-decomposition of subspaces and its role in characterizing Sp(n)-orbits. Discover how principal angles and cosines of special vector pairs contribute to the full set of invariants for k-dimensional subspaces in GR(k, 4n). Gain insights into the application of these concepts in complex geometry and symplectic group theory.