Modular representation algebras

On the Representation Theory of Modular Hecke Algebras

Let G be a finite group with a split &V-pair of characteristic p. We shall be interested in (right) modules over the group algebra over a complete discrete valuation ring 0 of characteristic zero, its field of quotients K and its residual field k. We shall assume that k has characteristic p, and that K and k are splitting fields for all subgroups of G. For any O-lattice& we use the notations L ...

Identifications in Modular Group Algebras

Let G be a group, S a subgroup of G, and F a field of characteristic p. We denote the augmentation ideal of the group algebra FG by ω(G). The Zassenhaus-Jennings-Lazard series of G is defined by Dn(G) = G ∩ (1 + ω(G)). We give a constructive proof of a Theorem of Quillen stating that the graded algebra associated to FG is isomorphic as an algebra to the enveloping algebra of the restricted Lie ...

Modular Representations of Hecke Algebras

These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory of finite groups of Lie type and survey the recent results which complete the classification of the simple modules. These results rely on the theory of Kazhd...

Algebras Ii : Representation Theory

Representation theory is developed for the class of Galois algebras introduced recently by the authors. In particular, categories of Harish-Chandra modules are studied for integral Galois algebras which include generalized Weyl algebras, the universal enveloping algebra of gl n , the quantization and Yangians for gl 2 .

Topological Representation of Algebras