Summary: SIX LECTURES ON DELIGNE-LUSZTIG THEORY
Abstract. Lectures given by Raphael Rouquier in Hilary term,
Oxford, 2010. Notes of lectures 2, 3, 4 and 6 by Geordie Williamson,
lecture 5 by David Craven.
1. Lecture 1
Here the example of SL2 was considered in detail and the character
table was discussed.
2. Lecture 2: Finite groups of Lie type
Fix k = k.
Algebraic group (affine) over k is an affine algebraic smooth variety
G endowed with a group structure.
Consider the algebra of regular functors k[G] on G. Then G =
Spec k[G] and k[G] is a (commutative) Hopf algebra.
Example 2.1. · Ga = Spec k[T], Ga(k) = k as an additive group.
· Gm = Spec k[T, T-1
], Ga(k) = k
These are all the one-dimensional groups.
· GLn = Spec k[Tij]1i,jn[det(Tij)-1
], GLn(k) consists of invert-