[ Seminar 2007 | Past Seminars ]
| Place: | Usually Room 126 (this year) Graduate School of Mathematical Sciences, the University of Tokyo [ Access ] |
| Date: | May 17 (Thu), 2007, 15:00-16:30 |
| Place: | Room 002, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Gen Mano (真野 元) (University of Tokyo) |
| Title: | The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q) |
| Abstract: [ pdf ] |
The indefinite orthogonal group O(p,q) (p+q even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the L2-model of the minimal representation of O(p,q) was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the G-action on L2(C). Our proof uses the Radon transform of distributions supported on the light cone. This is a joint work with T. Kobayashi. |
| Remark: | いつもと時刻・部屋が違います。ご注意ください。 |
| Date: | May 22 (Tue), 2007, 16:30-18:00 |
| Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Chifune Kai (甲斐千舟) (Kyushu University) |
| Title: | A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps |
| Abstract: [ pdf ] |
When a regular open convex cone is given, a natural partial order is introduced into the ambient vector space. If we consider the cone of positive numbers, this partial order is the usual one, and is reversed by taking inverse numbers in the cone. In general, for every symmetric cone, the inverse map of the associated Jordan algebra reverses the order. In this talk, we investigate this order-reversing property in the class of homogeneous convex cones which is much wider than that of symmetric cones. We show that a homogeneous convex cone is a symmetric cone if and only if the order is reversed by the Vinberg's *-map, which generalizes analytically the inverse maps of Jordan algebras associated with symmetric cones. Actually, our main theorem is formulated in terms of the family of pseudoinverse maps including the Vinberg's *-map as a special one. While our result is a characterization of symmetric cones, also we would like to mention O. Güler's result that for every homogeneous convex cone, some analogous pseudoinverse maps always reverse the order. |
| Date: | May 29 (Tue), 2007, 16:30-18:00 |
| Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Karl-Hermann Neeb (Technische Universität Darmstadt) |
| Title: | A host algebra for the regular representations of the canonical commutation relations |
| Abstract: [ pdf ] |
We report on joint work with H. Grundling (Sydney). The concept of a host algebra generalises that of a group C *-algebra to groups which are not locally compact in the sense that its non-degenerate representations are in one-to-one correspondence with representations of the group under consideration. A full host algebra covering all continuous unitary representations exist for an abelian topological group if and only if it (essentially) has a locally compact completion. Therefore one has to content oneselves with certain classes of representations covered by a host algebra. We show that there exists a host algebra for the set of continuous representations of the countably dimensional Heisenberg group corresponding to a non-zero central character. |
| Remark: | Neeb 教授は５月２６日（土）・２７日（日）に 東京大学で行われる第２回高木レクチャーで招待講演をされます。 こちらもどうぞご参加ください。 |
| Date: | June 19 (Tue), 2007, 16:30-18:00 |
| Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Yoshishige Haraoka (原岡喜重) (Kumamoto University) |
| Title: | Rigid local systems, integral representations of their sections and connection coefficients |
| Abstract: [ pdf ] |
A local system on CP1-{finite points} is called physically rigid if it is uniquely determined up to isomorphisms by the local monodromies. We explain two algorithms to construct every physically rigid local systems. By applying the algorithms we obtain integral representations of solutions of the corresponding Fuchsian differential equation. Moreover we can express connection coefficients of the equation in terms of the integrals. These results will be applied to several differential equations arising from the representation theory. |
| Contact: | Toshio Oshima [ Email ] and Toshiyuki Kobayashi [ Email ] |
© Toshiyuki Kobayashi