By Cédric Bonnafé
Deligne-Lusztig concept goals to review representations of finite reductive teams by way of geometric equipment, and especially l-adic cohomology. many glorious texts current, with assorted ambitions and views, this thought within the basic environment. This ebook specializes in the smallest non-trivial instance, specifically the gang SL2(Fq), which not just offers the simplicity required for a whole description of the idea, but in addition the richness wanted for illustrating the main smooth aspects.
The improvement of Deligne-Lusztig thought used to be encouraged by way of Drinfeld's instance in 1974, and Representations of SL2(Fq) is predicated upon this instance, and extends it to modular illustration concept. To this finish, the writer uses primary result of l-adic cohomology. for you to successfully use this equipment, an actual research of the geometric houses of the motion of SL2(Fq) at the Drinfeld curve is carried out, with specific recognition to the development of quotients by way of numerous finite groups.
At the top of the textual content, a succinct evaluation (without facts) of Deligne-Lusztig idea is given, in addition to hyperlinks to examples proven within the textual content. With the supply of either a gradual creation and several other fresh fabrics (for example, Rouquier's theorem on derived equivalences of geometric nature), this publication should 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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