ar X iv : m at h / 05 05 06 3 v 1 [ m at h . SG ] 3 M ay 2 00 5 A SYMPLECTIC REALIZATION OF VAN DEN BAN ’ S CONVEXITY THEOREM

ar X iv : m at h / 05 05 06 3 v 2 [ m at h . SG ] 2 5 Se p 20 06 1 A symplectic approach to van den Ban ’ s convexity theorem

Let G be a complex semisimple Lie group and τ a complex antilinear involution that commutes with a Cartan involution. If H denotes the connected subgroup of τ-fixed points in G, and K is maximally compact, each H-orbit in G/K can be equipped with a Poisson structure as described by Evens and Lu. We consider sym-plectic leaves of certain such H-orbits with a natural Hamiltonian torus action. A s...

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 06 05 37 9 v 1 [ m at h . R A ] 1 5 M ay 2 00 6 AN EXTENDED FREUDENTHAL MAGIC SQUARE IN CHARACTERISTIC 3

Date: May 15, 2006. 2000 Mathematics Subject Classification. Primary 17B25.

ar X iv : m at h / 06 05 37 3 v 1 [ m at h . A G ] 1 5 M ay 2 00 6 FLATNESS OF THE LINKED GRASSMANNIAN

We show that the linked Grassmannian scheme, which arises in a functorial compactification of spaces of limit linear series, and in local models of certain Shimura varieties, is Cohen-Macaulay, reduced, and flat. We give an application to spaces of limit linear series.

ar X iv : m at h / 05 06 06 8 v 1 [ m at h . G R ] 3 J un 2 00 5 ALGORITHM FOR LANG ’ S THEOREM

We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie type. We use an algorithm for computing a Chevalley basis for a split reductive Lie algebra, which is of independent interest.