# Thanasin Nampaisarn

## "Category $$\bar{\mathcal{O}}$$ for root reductive Lie Algebras, Part II"

 Date: Thu, October 12, 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.