Strongly Nilpotent Matrices and a Generalization of a Theorem of Konstant

Mark Colarusso
University of South Alabama
Assistant Professor of Mathematics

“Consider the set of n x n complex, nilpotent matrices with the property that every submatrix in the top left-hand corner is also nilpotent. We call such matrices strongly nilpotent. They play an important role in applied linear algebra, representation theory, and geometry. In this talk, we investigate the interaction between the geometry of strongly nilpotent matrices and representation theory. We show how this connection can be used to solve problems in noncommutative algebra and algebraic geometry. In particular, we generalize a basic theorem of Kostant that an enveloping algebra of a Lie algebra is free over its centre to the setting of Gelfand-Zeitlin theory. If time permits, we will discuss nonlinear versions of this result for Poisson Lie groups and finite W-algebras”.

Light refreshments will be served @ 1:30pm EMS E424A.

View Colarusso’s Event Flyer