Many aspects of the representation theory of a Lie algebra and its associated algebraic group are governed by the geometry of their nilpotent cone. In this talk, we will introduce an analogue of the nilpotent cone N for Lie superalgebras and show that for a simple classical Lie superalgebra the number of nilpotent orbits is finite. We will also show that the commuting variety X described by Duflo and Serganova, which has applications in the study of the finite-dimensional representation theory of Lie superalgebras, is contained in N. Consequently, the finiteness result on N generalizes and extends the work on the commuting variety.
This video is part of the University of Georgia‘s Algebra seminar.
