Parabolically induced representations of graded Hecke algebras

We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained with induction from a discrete series representation of a parabolic subalgebra. We determine all intertwining operators between such parabolically induced representations, and use them to parametrize the irreducible representations.Comment: In the second version several new results have been added to prove some claims from the last page of the first version. In the third version the introduction has been extended and we determine the global dimension of a graded Hecke algebr

Evolutionary Patterns of Bone Histology and Bone Compactness in Xenarthran Mammal Long Bones

Bone microstructure reflects physiological characteristics and has been shown to contain phylogenetic and ecological signals. Although mammalian long bone histology is receiving increasing attention, systematic examination of the main clades has not yet been performed. Here we describe the long bone microstructure of Xenarthra based on thin sections representing twenty-two species. Additionally, patterns in bone compactness of humeri and femora are investigated. The primary bone tissue of xenarthran long bones is composed of a mixture of woven, parallel-fibered and lamellar bone. The vascular canals have a longitudinal, reticular or radial orientation and are mostly arranged in an irregular manner. Concentric rows of vascular canals and laminar organization of the tissue are only found in anteater bones. The long bones of adult specimens are marked by dense Haversian bone, a feature that has been noted for most groups of mammals. In the long bones of armadillos, secondary osteons have an oblique orientation within the three-dimensional bone tissue, thus resulting in their irregular shape when the bones are sectioned transversely. Secondary remodeling is generally more extensive in large taxa than in small taxa, and this could be caused by increased loading. Lines of arrested growth are assumed to be present in all specimens, but they are restricted to the outermost layer in bones of armadillos and are often masked by secondary remodeling in large taxa. Parameters of bone compactness show a pattern in the femur that separates Cingulata and Pilosa (Folivora and Vermilingua), with cingulates having a lower compactness than pilosans. In addition, cingulates show an allometric relationship between humeral and femoral bone compactness