Modular representations of Hecke algebras of type G(p,p,n)

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...

Representations of Graded Hecke Algebras

Representations of affine and graded Hecke algebras associated to Weyl groups play an important role in the Langlands correspondence for the admissible representations of a reductive p-adic group. We work in the general setting of a graded Hecke algebra associated to any real reflection group with arbitrary parameters. In this setting we provide a classification of all irreducible representatio...

Representations of Hecke Algebras and Nite Groups of Lie Type

On Representations of Affine Hecke Algebras of Type B

Ariki’s and Grojnowski’s approach to the representation theory of affine Hecke algebras of type A is applied to type B with unequal parameters to obtain – under certain restrictions on the eigenvalues of the lattice operators – analogous multiplicity-one results and a classification of irreducibles with partial branching rules as in type A.

A Class of Representations of Hecke Algebras

A type of directed multigraph called aW -digraph is introduced to model the structure of certain representations of Hecke algebras, including those constructed by Lusztig and Vogan from involutions in a Weyl group. Building on results of Lusztig, a complete characterization of W -digraphs is given in terms of subdigraphs for dihedral parabolic subgroups. In addition, results are obtained relati...