Automorphisms of Grassmannians

Michael J. Cowen
1989 Proceedings of the American Mathematical Society  
For a complex vector space y of dimension n , the group of holomorphic automorphisms of the Grassmannian Gr(p, "V) can be identified with the subgroup of P Gl(/\p "V) preserving the Grassmannian. Using this, Chow showed K\x\(Qr(p,T)) = PG1(2^) for n ± 2p , and PGl(^) is a normal subgroup of index 2 in AuX(Gr(p,T~)) for n = 2p . We prove a version of Chow's result for a separable Hubert space.%". Theorem. P G\(ß?) is the subgroup of VG\(/\P ßt) which preserves Gr(p,^). That is, if R is an
more » ... , if R is an invertible linear operator on Af %? which preserves decomposable p-vectors, then there exists 5 , an invertible linear operator on ??, such that R = /\p S . _ -r
doi:10.2307/2047380 fatcat:wlhpkkutpfabbnv7qrm52foa5y