Linear representations of finite sets
Event details
| Date | 20.11.2019 |
| Hour | 15:15 › 16:30 |
| Speaker | Jacques Thévenaz, EPFL |
| Location | |
| Category | Conferences - Seminars |
Groups, Arithmetic and Algebraic Geometry Seminar
Abstract : A correspondence between two finite sets is a subset of their direct product. Correspondences can be composed and this gives rise to the category C of finite sets and correspondences. In a joint work with Serge Bouc, we study the linear representations of the category C, which turn out to have many remarkable features. In particular, we shall explain how the simple representations are parametrized in terms of finite posets. We shall sketch how to solve the difficult problem of finding the dimension of every evaluation of such a simple representation. Finally, we shall describe precisely all the posets for which the associated simple representations are projective. In the first part of the seminar, some elementary results on the simple representations of a small category will be explained and the special case of the representations of C will be considered. In the second part, more details will be given about the connection with finite posets.
Abstract : A correspondence between two finite sets is a subset of their direct product. Correspondences can be composed and this gives rise to the category C of finite sets and correspondences. In a joint work with Serge Bouc, we study the linear representations of the category C, which turn out to have many remarkable features. In particular, we shall explain how the simple representations are parametrized in terms of finite posets. We shall sketch how to solve the difficult problem of finding the dimension of every evaluation of such a simple representation. Finally, we shall describe precisely all the posets for which the associated simple representations are projective. In the first part of the seminar, some elementary results on the simple representations of a small category will be explained and the special case of the representations of C will be considered. In the second part, more details will be given about the connection with finite posets.
Practical information
- Informed public
- Free
Organizer
- Donna Testerman
Contact
- Maroussia Schaffner