Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations

We present a necessary and sufficient condition for a finite-dimensional highest weight representation of the $sl_2$ loop algebra to be irreducible. In particular, for a highest weight representation with degenerate parameters of the highest weight, we can explicitly determine whether it is irreducible or not. We also present an algorithm for constructing finite-dimensional highest weight representations with a given highest weight. We give a conjecture that all the highest weight representations with the same highest weight can be constructed by the algorithm. For some examples we show the conjecture explicitly. The result should be useful in analyzing the spectra of integrable lattice models related to roots of unity representations of quantum groups, in particular, the spectral degeneracy of the XXZ spin chain at roots of unity associated with the $sl_2$ loop algebra.Comment: 32 pages with no figure; with corrections on the published versio

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Advances in progenitor cell therapy using scaffolding constructs for central nervous system injury.

Traumatic brain injury (TBI) is a major cause of morbidity and mortality in the United States. Current clinical therapy is focused on optimization of the acute/subacute intracerebral milieu, minimizing continued cell death, and subsequent intense rehabilitation to ameliorate the prolonged physical, cognitive, and psychosocial deficits that result from TBI. Adult progenitor (stem) cell therapies have shown promise in pre-clinical studies and remain a focus of intense scientific investigation. One of the fundamental challenges to successful translation of the large body of pre-clinical work is the delivery of progenitor cells to the target location/organ. Classically used vehicles such as intravenous and intra arterial infusion have shown low engraftment rates and risk of distal emboli. Novel delivery methods such as nanofiber scaffold implantation could provide the structural and nutritive support required for progenitor cell proliferation, engraftment, and differentiation. The focus of this review is to explore the current state of the art as it relates to current and novel progenitor cell delivery methods