Date:	Thu, April 27, 2017
Time:	11:30
Place:	Seminar Room (120), Research I

Abstract: Let \(\bar{\mathcal{O}}\) denote the extended category \(\mathcal{O}\) of a root-reductive Lie algebra \(\mathfrak{g}\) with respect to a splitting Borel subalgebra \(\mathfrak{b}\). An object \(M\) in \(\bar{\mathcal{O}}\) may have infinite length. In fact, it can even be an uncountable direct sum of indecomposable submodules. Despite this problem, \(M\) has a generalized composition series, which is an analogue of the standard composition series for modules of finite length. In this talk, we shall prove the existence and the uniqueness of generalized composition series of an object \(M\in\bar{\mathcal{O}}\).