Back to Departmental Colloquium: Fall 2009
Departmental Colloquium
Date: Thursday, Nov 12, 2009
Time: 4:15PM
Location: JWB 335
Anthony Henderson
University of Sydney
Title |
Enhancing the Jordan canonical form |
Abstract |
In undergraduate linear algebra, we learned the Jordan canonical form theorem: that every n x n complex matrix A is similar to an essentially unique matrix B which is block-diagonal with each block having a very simple form (a single eigenvalue repeated down the diagonal, ones on the super-diagonal, and zeroes elsewhere). This is of course very useful for matrix calculations. From the Lie-theoretic viewpoint, this theorem is about classifying the orbits of the general linear group GL_n(C) in its adjoint representation. This suggests natural follow-up questions about the closures of the orbits. It also raises the hope of finding analogous orbit classifications for other representations of algebraic groups. After explaining some of the general context, I will focus on a case which, despite its close proximity to the Jordan canonical form theorem, has only recently been worked out: the direct sum of the vector and adjoint representations of GL_n(C). This is joint work with Pramod Achar (Louisiana State University). |
Representation Theory