Admissible characters were introduced by Harish-Chandra in the 1950’s. Any admissible character is equal to a finite sum of characters of irreducible (typically) infinite dimensional representations of a real reductive algebraic group, G. The abelian group of admissible characters is an infinite rank free group on the so-called standard characters, which were calculated explicitly as of the 1980’s. Kazhdan, Lusztig and Vogan discovered an algoritm for computing irreducible characters as integral combinations of standard characters. Speh, Vogan and Zuckerman reduced this computation to a finite calculation for each group G. The Atlas of Lie Groups Project has now implemented this finite algoritm for all groups of complex rank less than or equal to eight.
By far the most difficult case is the split real form of type E8. The numerical data for this group would cover an area the size of Manhatten Island! The calculation required a supercomputer and a great deal of programming genius. Information can be obtained at www.aimath.org. We will discuss the broad outline of theory of admissible characters and try to explain why the E8 breakthrough generated so much positive publicity for Lie Group Theory.
The symmetric spaces of split exceptional groups arise in the theory of the dimensional reduction of supergravity theory and M-theory in eleven dimensions. We will speculate on the implications of the Atlas of Lie Groups Project for the nexus of geometry, symmetry and physics.