Character Tables for Exceptional Real Reductive Groups

This is the third of a series of lectures about character
tables and the Atlas of Lie Groups. First we will explain the role of the so-called Translation Principle for representations and characters of reductive groups. We will then describe the Kazhdan-Lusztig-Vogan algorithm for computing the change of basis from irreducible characters to standard characters. We will report on the explicit output of the KLV algorithm for real reductive groups of exceptional type. The Atlas Project generated this enormous output using a combination of a supercomputer and a highly ingenious computational strategy. Background on this computation can be found at aimath.org.