P-ADIC LATTICES OF PSEUDO REFLECTION GROUPS

                       D. Notbohm
Let U be a vector space over the $p$--adic rationals,
and let $W --> Gl(U)$ be faithful representation of a finite group 
such that $W$ is generated by pseudo reflections. 
For odd primes we study the $p$-adic $W$-sublattice  of this representation and achieve a complete classification. Examples of such situations are given by
the Weyl group acting on the 1-dimesional homology of the maximal torus of 
a compact connected Lie group, or of the so called 
$p$--compact groups, a homotopy theoretic 
generalisation of compact Lie groupss. The associated lattices are an 
important algebraic
invariant  in the study of these geometric object.