Sheaves on buildings and modular representations of chevalley groups

Modular sheaves and representations

Kazhdan-laumon Representations of Chevalley Groups, Character Sheaves and Some Generalization of the Lefschetz-verdier Trace Formula

Let G be a reductive group over a finite field Fq and let G(Fq) be its group of Fq-rational points. In 1976 P. Deligne and G. Lusztig (following a suggestion of V. Drinfeld for G = SL(2)) associated to any maximal torus T in G defined over Fq certain remarkable series (virtual) representations of the group G(Fq). These representations were realized in é tale l-adic cohomology of certain algebra...

Lectures on Chevalley Groups

( b ) H is maximal n i l p o t e n t and every subgroup of f i n i t e l a d e x . . i s of f i n i t e index i n i t s normalizer. Proof of Theorem 6: ( a ) Map Ga -> #, by x,: t -> x,(t) . This is a r a t i o n a l homomorphism. So s i n c e Ga i s a connected , ~ g e b r a i c group s o i s Xa . Hence G is a lgebra ic and connected.. Let R = r a d G . Since R is so lvable and normal it i s f...

Small degree representations of finite Chevalley groups in defining characteristic

We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l3 and for rank 11 m...

Modular Representations of Symmetric Groups

Over the last few weeks, we have seen lots of things in representation theory—we began by looking at an onslaught of examples to see explicitly what representations look like, we discussed character theory and looked at character tables, we talked about representations from a module-theoretic perspective, and then we saw how we can model the representation theory of the symmetric group via the ...