Speaker : Prof. Kevin Coulembier (University of Sydney) Title : Infinite limits of BGG category $\mathcal O$ Time : 2018-01-12 (Fri) 15:00 - 16:00 Place : Seminar Room 722, Institute of Mathematics (NTU Campus) Abstract: It is possible to take various limits of BGG category $\mathcal O$ for finite simple Lie algebras of a fixed type with their rank going to infinity. This is already useful for studying original category $\mathcal O$, but has also led to breakthroughs in representation theory of Lie superalgebras, by the concept of ‘super duality’, which establishes connections between Lie algebras and Lie superalgebras at infinity. Motivated by these theories, we are developing a systematic study of category $\mathcal O$ for finitary Lie algebras such as gl(infinity). I will introduce the basic set-up and discuss some results on Ringel and Koszul duality, homological properties and decomposition multiplicities. This is based on joint work with Ivan Penkov.