Lie Groups and Representation Theory

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2008/01/15

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Fulton Gonzalez (Tufts University)
Group contractions, invariant differential operators and the matrix Radon transform

[ Abstract ]
Let $M_{n,k}$ denote the vector space of real $n\\times k$ matrices.
The matrix motion group is the semidirect product $(\\text O(n)\\times \\text O(k))\\ltimes M_{n,k}$, and is the Cartan motion group
associated with the real Grassmannian $G_{n,n+k}$.
The matrix Radon transform is an
integral transform associated with a double fibration involving
homogeneous spaces of this group. We provide a set of
algebraically independent generators of the subalgebra of its
universal enveloping algebra invariant under the Adjoint
representation. One of the elements of this set characterizes the range of the matrix Radon transform.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html