329 research outputs found
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
The characteristic identity formalism discussed in our recent articles is
further utilized to derive matrix elements of type 2 unitary irreducible
modules. In particular, we give matrix element formulae for all
gl(m|n) generators, including the non-elementary generators, together with
their phases on finite dimensional type 2 unitary irreducible representations.
Remarkably, we find that the type 2 unitary matrix element equations coincide
with the type 1 unitary matrix element equations for non-vanishing matrix
elements up to a phase.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.424
Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
In this paper fundamental Wigner coefficients are determined algebraically by
considering the eigenvalues of certain generalized Casimir invariants. Here
this method is applied in the context of both type 1 and type 2 unitary
representations of the Lie superalgebra gl(mjn). Extensions to the non-unitary
case are investigated. A symmetry relation between two classes of Wigner
coefficients is given in terms of a ratio of dimensions.Comment: 17 page
Casimir Invariants from Quasi-Hopf (Super)algebras
We show how to construct, starting from a quasi-Hopf (super)algebra, central
elements or Casimir invariants. We show that these central elements are
invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum
(super)groups, which arise from twisting the normal quantum (super)groups, have
the same Casimir invariants as the corresponding quantum (super)groups.Comment: 24 pages, Latex fil
Characteristic identities for Lie (super)algebras
We present an overview of characteristic identities for Lie algebras and
superalgebras. We outline methods that employ these characteristic identities
to deduce matrix elements of finite dimensional representations. To demonstrate
the theory, we look at the examples of the general linear Lie algebras and Lie
superalgebras.Comment: 10 pages, contribution to the 30th International Colloquium on Group
Theoretical Methods in Physics (Group30) in Ghent, Belgium. Journal of
Physics: Conference Series (to appear
Architecture Optimization Dramatically Improves Reverse Bias Stability in Perovskite Solar Cells: A Role of Polymer Hole Transport Layers
We report that device architecture engineering has a substantial impact on
the reverse bias instability that has been reported as a critical issue in
commercializing perovskite solar cells. We demonstrate breakdown voltages
exceeding -15 V in typical pin structured perovskite solar cells via two steps:
i) using polymer hole transporting materials; ii) using a more
electrochemically stable gold electrode. While device degradation can be
exacerbated by higher reverse bias and prolonged exposure, our as-fabricated
perovskite solar cells completely recover their performance even after
stressing at -7 V for 9 hours both in the dark and under partial illumination.
Following these observations, we systematically discuss and compare the reverse
bias driven degradation pathways in perovskite solar cells with different
device architectures. Our model highlights the role of electrochemical reaction
rates and species in dictating the reverse bias stability of perovskite solar
cells
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations.We compare our results with existingworks that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities
The ‘mosaic habitat’ concept in human evolution: past and present
The habitats preferred by hominins and other species are an important theme in palaeoanthropology, and the ‘mosaic habitat’ (also referred to as habitat heterogeneity) has been a central concept in this regard for the last four decades. Here we explore the development of this concept – loosely defined as a range of different habitat types, such as woodlands, riverine forest and savannah within a limited spatial area– in studies of human evolution in the last sixty years or so. We outline the key developments that took place before and around the time when the term ‘mosaic’ came to wider palaeoanthropological attention. To achieve this we used an analysis of the published literature, a study of illustrations of hominin evolution from 1925 onwards and an email survey of senior researchers in palaeoanthropology and related fields. We found that the term mosaic starts to be applied in palaeoanthropological thinking during the 1970’s due to the work of a number of researchers, including Karl Butzer and Glynn Isaac , with the earliest usage we have found of ‘mosaic’ in specific reference to hominin habitats being by Adriaan Kortlandt (1972). While we observe a steady increase in the numbers of publications reporting mosaic palaeohabitats, in keeping with the growing interest and specialisation in various methods of palaeoenvironmental reconstruction, we also note that there is a lack of critical studies that define this habitat, or examine the temporal and spatial scales associated with it. The general consensus within the field is that the concept now requires more detailed definition and study to evaluate its role in human evolution
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