By Cédric Bonnafé
Deligne-Lusztig conception goals to check representations of finite reductive teams through geometric tools, and especially l-adic cohomology. many glorious texts current, with various objectives and views, this conception within the common environment. This booklet specializes in the smallest non-trivial instance, particularly the crowd SL2(Fq), which not just offers the simplicity required for an entire description of the speculation, but additionally the richness wanted for illustrating the main tender aspects.
The improvement of Deligne-Lusztig thought was once encouraged by way of Drinfeld's instance in 1974, and Representations of SL2(Fq) relies upon this instance, and extends it to modular illustration conception. To this finish, the writer uses primary result of l-adic cohomology. so one can successfully use this equipment, an exact learn of the geometric homes of the motion of SL2(Fq) at the Drinfeld curve is performed, with specific realization to the development of quotients through quite a few finite groups.
At the tip of the textual content, a succinct review (without evidence) of Deligne-Lusztig idea is given, in addition to hyperlinks to examples established within the textual content. With the availability of either a gradual advent and several other fresh fabrics (for example, Rouquier's theorem on derived equivalences of geometric nature), this booklet should be of use to graduate and postgraduate scholars, in addition to researchers and academics with an curiosity in Deligne-Lusztig theory.