ar X iv : m at h / 04 06 05 4 v 1 [ m at h . FA ] 3 J un 2 00 4 SPECIAL STANDARD STATIC SPACE - TIMES 1

ar X iv : m at h / 02 06 04 1 v 3 [ m at h . FA ] 5 O ct 2 00 2 Abstract harmonic analysis , homological algebra , and operator spaces

harmonic analysis, homological algebra, and operator spaces

ar X iv : m at h / 02 06 04 1 v 2 [ m at h . FA ] 9 S ep 2 00 2 Abstract harmonic analysis , homological algebra , and operator spaces

harmonic analysis, homological algebra, and operator spaces

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 04 05 8 v 1 [ m at h . FA ] 4 A pr 2 00 6 SPHERICAL HARMONIC ANALYSIS ON AFFINE BUILDINGS

Let X be a locally finite regular affine building with root system R. There is a commutative algebra A spanned by averaging operators A λ , λ ∈ P + , acting on the space of all functions f : V P → C, where V P is in most cases the set of all special vertices of X , and P + is a set of dominant coweights of R. This algebra is studied in [6] and [7] for˜An buildings, and the general case is treat...

ar X iv : m at h / 06 06 07 4 v 1 [ m at h . R T ] 3 J un 2 00 6 On the Divided Power Algebra and the Symplectic Group in Characteristic 2

Let V be an even dimensional vector space over a field K of characteristic 2 equipped with a non-degenerate alternating bilinear form f . The divided power algebra DV is considered as a complex with differential defined from f . We examine the cohomology modules as representations of the corresponding symplectic group.