Alice Barbara Tumpach
The restricted Grassmannian and its cotangent space from various point of views
This talk is divided into two parts. First, the construction of the restricted Grassmannian as symplectic and Kähler quotient is revisited in the language of frame theory. In this context, the set of $k$-tight frames which are unitary equivalent for the Hilbert–Schmidt norm to a fixed $k$-tight frame corresponds to a level set of the momentum map. In the second part of the talk we "double" the dimension and construct the cotangent space of the restricted Grassmannian as a tri-symplectic and hyper-Kähler quotient. The diffeomorphism between the cotangent space of the restricted Grassmannian and the complexification of the restricted Grassmannian following from Mostow's decomposition theorem will be explained. The Kähler potentials for various complex structures will be given. This talk is based on a joint work with T. Goliński, T. Needham and C. Shonkwiler.
