Eliana Zoque

Abstract: Two matrices X and Y are said to be almost commuting if rk[X,Y]≤1. Gan and Ginzburg studied the structure of the variety M={(X,Y,i,j) ∈ g × g × V × V^* | [X,Y]+ij=0} (where V is an n-dimensional vector space over C) and found its connected components. In this talk we describe the conjugacy classes and the isotropy of N={(X,Y,i,j) ∈ g × g × V × V^* | [X,Y]+ij=0; X and Y are nilpotent} under the action by GL_n and conjecture that N has n irreducible components: 2 corresponding to the case where the matrices commute, and n-2 corresponding to the noncommutative pairs. Our approach uses the tools that Baranovsky used to prove that the variety of commuting nilpotent matrices is irreducible: we consider a map from N to appropiate Hilbert spaces of points.

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.