Deligne-Lusztig theory aims to study representations of finite
reductive groups by means of geometric methods, and particularly
l-adic cohomology. Many excellent texts present, with different
goals and perspectives, this theory in the general setting. This
book focuses on the smallest non-trivial example, namely the group
SL2(Fq), which not only provides the simplicity required for a
complete description of the theory, but also the richness needed
for illustrating the most delicate aspects.
The development of Deligne-Lusztig theory was inspired by
Drinfeld's example in 1974, and Representations of SL2(Fq) is based
upon this example, and extends it to modular representation theory.
To this end, the author makes use of fundamental results of l-adic
cohomology. In order to efficiently use this machinery, a precise
study of the geometric properties of the action of SL2(Fq) on the
Drinfeld curve is conducted, with particular attention to the
construction of quotients by various finite groups.
At the end of the text, a succinct overview (without proof) of
Deligne-Lusztig theory is given, as well as links to examples
demonstrated in the text. With the provision of both a gentle
introduction and several recent materials (for instance, Rouquier's
theorem on derived equivalences of geometric nature), this book
will be of use to graduate and postgraduate students, as well as
researchers and lecturers with an interest in Deligne-Lusztig
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!