The Auslander conjecture for dimension less than 7

In 1967 L. Auslander conjectured that every crystallographic subgroup of an affine group is virtually solvable, i.e. contains a solvable subgroup of finite index. D. Fried and W. Goldman proved Auslander's conjecture for affine space of dimension 3 using cohomological arguments. Using dynamical arguments we prove the Auslander conjecture for dimension less than 7.Comment: This paper has been withdrawn by the author due to corrections. We added acknowledgement

Extreme rays of the (N,k)(N, k)-Schur Cone

We discuss several partial results towards proving Dennis White's conjecture on the extreme rays of the $(N,2)$-Schur cone. We are interested in which vectors are extreme in the cone generated by all products of Schur functions of partitions with $k$ or fewer parts. For the case where $k =2$, White conjectured that the extreme rays are obtained by excluding a certain family of "bad pairs," and proved a special case of the conjecture using Farkas' Lemma. We present an alternate proof of the special case, in addition to showing more infinite families of extreme rays and reducing White's conjecture to two simpler conjectures.Comment: This paper has been withdrawn by the authors due to a misinterpretation of the generalized Littlewood-Richardson rule in several proof