CU Algebraic Lie Theory Seminar

Modified Exponential Maps and the Finite Group of Unipotent Uppertriangular Matrices

Rachel Krieger, CU

April 14, 2009
1-2pm
Math 220

Abstract

A supercharacter theory of the finite group of unipotent uppertriangular matrices U_n(F_q) has been developed based on the existence of an underlying nilpotent associative algebra. In this talk, we consider a family of maps between the nilpotent associative algebra and U_n(F_q). We first determine a method by which the image of any element in the algebra can be computed. We then show that the particular map chosen does not affect the location of the two-sided orbit, so that the superclasses defined in this way are independent of the map between the underlying algebra and the group. Hence, the superclasses arising in this particular supercharacter theory may have another natural definition for Chevalley groups.