groups 
Tilting modules for classical groups and howe duality in positive characteristics


We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.


The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the nonarithmetic lattices inSO(n,1) constructed by Gromov and PiatetskiShapiro [GPS] and to groups generated by reflections.


Affine weyl groups and conjugacy classes in Weyl groups


Presentations for crystallographic complex reflection groups


The presentations are given in the form of graphs resembling Dynkin diagrams and very similar to the presentations for finite complex reflection groups given in [2].


As in the case of affine Weyl groups, they can be obtained by adding a further node to the diagram for the linear part.


Invariant analytic domains in complex semisimple groups


We study the multiplicative structure of rings of coinvariants for finite groups.


Some curious Kleinian groups and hyperbolic 5manifolds


The finite irreducible linear groups with polynomial ring of invariants


For the case of positive characteristic we use the classification of finite irreducible groups generated by pseudoreflections due to Kantor, Wagner, Zalesski? and Sere?kin.


This allows us to obtain a complete list of all irreducible linear groups with a polynomial ring of invariants.


Compactness propertiesCn andC Pn for locally compact groupsG are introduced generalizing the finiteness propertiesFn andF Pn for discrete groups.


Classical invariant theory for finite reflection groups


We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups).


We conjecture that this is also true for the exceptional reflection groups and then sketch a proof for the group of typeF4.


A localglobal principle for finiteness properties ofSarithmetic groups over number fields


In the preceding paper [AT] compactness propertiesCn andCPn for locally compact groups were introduced.


They generalize the finiteness propertiesFn andFPn for discrete groups.

