Double coset decomposition for SL(r + s, Z) with respect to congruence subgroups

Cuspidal Cohomology for Principal Congruence Subgroups of Gl(3, Z)

The cohomology of arithmetic groups is made up of two pieces, the cuspidal and noncuspidal parts. Within the cuspidal cohomology is a subspace— the /-cuspidal cohomology—spanned by the classes that generate representations of the associated finite Lie group which are cuspidal in the sense of finite Lie group theory. Few concrete examples of /-cuspidal cohomology have been computed geometrically...

Group Decomposition by Double Coset Matrices

A generalized Cartan decomposition for the double coset space

Motivated by recent developments on visible actions on complex manifolds, we raise a question whether or not the multiplication of three subgroups L, G and H surjects a Lie group G in the setting that G/H carries a complex structure and contains G/G ∩ H as a totally real submanifold. Particularly important cases are when G/L and G/H are generalized flag varieties, and we classify pairs of Levi ...

On the cohomology of congruence subgroups of SL4 (Z)

We survey our joint work with Avner Ash and Mark McConnell that computationally investigates the cohomology of conguence subgroups of SL4(Z).

Cohomology of congruence subgroups of SL(4,Z) II

In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4(Z), J. Number Theory 94 (2002) 181–212] we computed cohomology groups H (Γ0(N),C), where Γ0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N . In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and addi...