2011 AMS Levi L. Conant Prize Recipient
THE CHARACTER TABLE OF E8(ℝ)
Abstract: In 2007, a group of about 20 mathematicians completed the computation of character tables for all the real forms of the exceptional Lie groups, using algorithms introduced by Kazhdan and Lusztig nearly 30 years ago. In the case of the 248-dimensional group called E8(ℝ), the character table (in a very compressed form) occupies about 50 gigabytes of disk space. I’ll talk about several (closely related) questions:
Since these groups have infinitely many conjugacy classes and infinitely many representations, how can one write a character table in finite terms?
What assurance is there that these enormous tables are correct?
How can one extract from them information that a human can understand and find interesting?
As a corollary of these investigations, I will also try to shed some light on the question of whether computers are animated by a demonic malevolence toward humanity.
David Vogan has been a member of the MIT faculty since 1979. He received his PhD from MIT in 1976, under the direction of Bertram Kostant. Most of his work concerns representation theory of Lie groups. He has written papers and books with 13 separate co-authors (an approach he recommends for its effect on Erdös number, for relief of writer’s cramp, for looking smarter, and for enjoying mathematics). He is a member of the American Academy of Arts and Sciences.