| Résume | The Weil representation is a well-known toolto study arithmetic and cohomological aspects of orthogonal groups.We construct certain, "special", cohomology classes for orthogonal groups$O(p,q)$ with coefficients in a finite dimensional representation anddiscuss their automorphic and geometric properties. In particular, theseclasses are generalizations of previous work of Kudla and Millson and giverise to Poincare dual forms for certain, "special", cycles withnon-trivial coefficients in arithmetic quotients of the associatedsymmetric space for the orthogonal group.Furthermore, we determine the behavior of these classes at the boundary ofthe Borel-Serre compactification of the associated locally symmetric space.As a consequence we are able to obtain new non-vanishing results for thespecial cycles.This is joint work with John Millson. |
