### Mathematics Colloquium

# Lucas Fresse

### (University of Lorraine, Nancy)

## "Cell decompositions for infinite-dimensional flag varieties"

** Date: ** |
Mon, October 26, 2015 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** A flag in a finite-dimensional vector space V is by definition a chain of subspaces of V. The flags of a given type (i.e., with prescribed dimensions) form an algebraic variety. This variety has a remarkable structure, for instance it has a decomposition into so-called Schubert cells. It plays an important role in the representation theory of the group GL(V). In the case of infinite-dimensional vector spaces, Dimitrov and Penkov introduced a notion of generalized flags, which allows to attach infinite-dimensional flag varieties to the classical ind-groups. In this talk, I will present an analogue of the Schubert decomposition in the infinite-dimensional setting. A significant difference with the finite-dimensional case is that many types of cell decompositions can be obtained, which is due to the fact that classical ind-groups admit many non-conjugate Borel subgroups. The talk is based on a joint work with Ivan Penkov.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*