The reflection representations of some Chevalley groups

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...

Representations of Chevalley Groups Arising from Admissible Lattices

The modules for a Chevalley group arising from admissible lattices in an irreducible module for the associated complex semisimple Lie algebra are studied. It is proved that the transpose of such a module is still in this collection and generically the cohomology modules of line bundles on the flag varieties are in this collection also. In the rank 1 case, all modules in this collection are inde...

Chow Rings and Cobordism of Some Chevalley Groups

We compute the cobordism rings of the classifying spaces of a certain class of Chevalley groups. In the particular case of the general linear group, we prove that it is isomorphic to the Chow ring.

Projective Representations of Reflection Groups Ii

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...