By Cédric Bonnafé
Deligne-Lusztig idea goals to review representations of finite reductive teams by way of geometric equipment, and especially l-adic cohomology. many glorious texts current, with various objectives and views, this concept within the basic surroundings. This publication 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 idea, but additionally the richness wanted for illustrating the main soft aspects.
The improvement of Deligne-Lusztig concept used to be encouraged by means of Drinfeld's instance in 1974, and Representations of SL2(Fq) is predicated upon this instance, and extends it to modular illustration idea. To this finish, the writer uses basic result of l-adic cohomology. to be able to 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 cognizance to the development of quotients via a variety of finite groups.
At the tip of the textual content, a succinct evaluation (without evidence) of Deligne-Lusztig concept is given, in addition to hyperlinks to examples validated within the textual content. With the supply of either a gradual advent and a number of other fresh fabrics (for example, Rouquier's theorem on derived equivalences of geometric nature), this ebook may be of use to graduate and postgraduate scholars, in addition to researchers and teachers with an curiosity in Deligne-Lusztig theory.
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Representations of SL2(Fq): 13 (Algebra and Applications) by Cédric Bonnafé