ALBERT

Notes: Abstract Multiple-angle-of-incidence (MAI) ellipsometry is used to study Ge x Si1−x /Si superlattices fabricated by a RRH/VLP-CVD system. Based on the fundamental ellipsometric equations and properties of semiconductor superlattices (SL), various parameters of SL structure, such as the sublayer thickness, complex refractive index and composition, are achieved precisely and simultaneously. The results obtained from ellipsometry are well consistent with those from growth conditions and other characterization techniques.

Notes: A spectral parameter-dependent solution of the graded Yang–Baxter equation is obtained, which is universal in the sense that it lives in Uq(gl(m/n))⊗End(V) with V the vector module of Uq(gl(m/n)). The invariants of this quantum supergroup are constructed using this solution.

Notes: The generalized Gel'fand invariants for an arbitrary quantum group are explicitly constructed, and their eigenvalues in any irreducible representation are computed. These invariants enable one to develop characteristic identities for the quantum group, and as a natural application, these identities are used to construct projection operators for tensor products of representations. To illustrate the general theory, the quantum group Uq(gl(m)) is studied in detail.

Notes: It is shown that from each self-dual representation of a quantum supergroup with nonvanishing q-superdimension, a graded representation of the Temperley–Lieb algebra can be constructed, which, in turn, gives rise to a solution of the graded Yang–Baxter equation. As examples, the vector irrep of Uq (osp(M/2n)) and all the finite-dimensional irreps of Uq (osp(1/2)) are studied, and the corresponding graded R-matrices are obtained explicitly. A general method is also given to obtain link polynomials from graded R-matrices. Applied to the ones associated with graded representations of the Temperley–Lieb algebra, the method yields the Jones polynomial.

Notes: A method for inducing nondegenerate forms on irreducible gl(m||n) modules that implies some general results on star and grade star representations is investigated. These results are applied to obtain a complete classification, in terms of highest weights, of the irreducible star and grade star representations of gl(n||1). It is demonstrated that while gl(n||1) admits a large class of star representations the irreducible grade star representations are comparatively rare. Moreover, for n≠2 all grade star irreducible representations are also star representations and, for n〉2, are atypical. The superalgebra gl(2||1) proves to be a special case and admits a two-parameter family of four-dimensional typical grade star irreducible representations that are not star representations. In particular, typical grade star irreducible representations of gl(n||1) exist only for n=1,2.

Notes: All the finite-dimensional star irreps of gl(m||n) are classified in terms of their highest weights, thereby completing the classification of all finite-dimensional star irreps of the basic classical Lie superalgebras. The lowest weights of such irreps are determined explicitly and it is shown that the contravariant and covariant tensor irreps of gl(m||n) are star irreps of type (1) and (2), respectively. This explains the applicability of the Young diagram method to these two classes of representations. However, it is shown that one-parameter families of typical star irreps occur that are intrinsically different from the tensorial irreps.

Notes: Ultramafic blocks that themselves contain eclogite lenses in the Triassic Su-Lu ultrahigh-P terrane of eastern China range in size from hundreds of metres to kilometres. The ultramafic blocks are enclosed in quartzofeldspathic gneiss of early Proterozoic age. Ultramafic rocks include garnetiferous lherzolite, wehrlite, pyroxenite, and hornblende peridotite. Garnet lherzolites are relatively depleted in Al2O3 (〈3.8wt%), CaO (〈3.2%) and TiO2 (〈0.11 wt%), and are low in total REE contents (several p.p.m.), suggesting that the rocks are residual mantle material that was subjected to low degrees of partial melting. The eclogite lenses or layers within the ultramafic rocks are characterized by higher MgO and CaO, lower Al2O3 and TiO2 contents, and a higher CaO/Al2O3 ratio compared to eclogites enclosed in the quartzofeldspathic gneiss. Scatter in the plots of major and trace elements vs. MgO, REE patterns and La, Sm and Lu contents suggest that some eclogites were derived from melts formed by various degrees (0.05–0.20) of partial melting of peridotite, and that other eclogites formed by accumulation of garnet and clinopyroxene ± trapped melt in the upper mantle.Both ultramafic and eclogitic rocks have experienced a complex metamorphic history. At least six stages of recrystallization occurred in the ultramafic rocks based on an analysis of reaction textures and mineral compositions. Stage I is a high temperature protolith assemblage of Ol + Opx + Cpx + Spl. Stage II consists of the ultrahigh-pressure assemblage Ol + Cpx + Opx + Grt. Stage III is manifested by the appearance of fine-grained garnet after coarse-grained garnet. Stage IV is characterized by formation of kelyphitic rims of fibrous Opx and Cpx around garnet, and replacement of garnet by spinel and pargasitic-hornblende. Stage V is represented by the assemblage Ol + Opx + Prg-Hbl + Spl. The mineral assemblages of stages VIA and VIB are Ol + Tr-Amp + Chl and Serp + Chl ± talc, respectively. Garnet and orthopyroxene all show a decrease in MgO with retrogressive recrystallization and Na2O in clinopyroxene also decreases throughout this history. Eclogites enclosed within ultramafic blocks consist of Grt + Omp + Rt ± Qtz ± Phn. A few quartz-bearing eclogites contain rounded and oval inclusion of polycrystalline quartz aggregates after coesite in garnet and omphacite. Minor retrograde features include thin symplectic rims or secondary amphiboles after Cpx, and ilmenite after rutile. P-T estimates indicate that the ultrahigh-metamorphism (stage II) of ultramafic rocks occurred at 820-900d̀ C and 36-41 kbar and that peak metamorphism of eclogites occurred at 730-900d̀ C and 〉28 kbar. Consonant with earlier plate tectonic models, we suggest that these rocks were underplated at the base of the continental crust. The rocks then underwent ultrahigh-pressure metamorphism and were tectonically emplaced into thickened continental crust during the Triassic collision between the Sino-Korean and Yangtze cratons.

Notes: Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n)) at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction. The representation theory is rather similar to that of gl(m/n) at generic q, but drastically different when q is a root of unity. In the latter case, atypicality conditions of highest weight irreducible representations (irreps) are substantially altered, and such finite-dimensional irreps arise that do not have highest weight and/or lowest weight vectors. As concrete examples, the irreps of Uq(gl(2/1)) are classified.

Notes: A method is developed for constructing multiparameter link invariants for a class of representations of the quantum supergroups Uq(gl(m||n)). The cases Uq(gl(1||1)) and Uq(gl(2||1)) are studied in detail. In the former we obtain a multiparameter generalization of the Alexander–Conway invariants.