### Seminar in Algebra, Lie Theory, and Geometry

# Thanasin Nampaisarn

### (Jacobs University Bremen)

## "Category \(\bar{\mathcal{O}}\) for root reductive Lie Algebras, Part I"

** Date: ** |
Thu, October 5, 2017 |

** Time: ** |
11:15 |

** Place: ** |
Seminar Room (120), Research I |

**Abstract:** Let \(\mathfrak{g}\) be a root-reductive Lie algebra over an algebraically closed field \(\mathbb{K}\) of characteristic \(0\) with a splitting Borel subalgebra \(\mathfrak{b}\) containing a splitting maximal toral subalgebra \(\mathfrak{h}\). We study the category \(\bar{\mathcal{O}}\) consisting of all \(\mathfrak{h}\)-weight \(\mathfrak{g}\)-modules which are locally \(\mathfrak{b}\)-finite and have finite-dimensional \(\mathfrak{h}\)-weight spaces. The focus is on very special Borel subalgebras called the Dynkin Borel subalgebras. This talk serves as an initial passage to the understanding of categories \(\mathcal{O}\) for infinite-dimensional root-reductive Lie algebras.