On complete reducibility for infinite-dimensional Lie algebras

In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.Comment: 63 pages; the proof of Lemma 1.3.1 is change

Characters of (relatively) integrable modules over affine Lie superalgebras

In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [bar over g]-module F(L), where [bar over g] is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight [bar over g]-module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional g-modules when g is basic, and all maximally atypical non-critical integrable g-modules when g is affine with non-zero dual Coxeter number.Simons Foundation. Postdoctoral Fellowshi

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic

NASA-JSC Protocol for the Characterization of Single Wall Carbon Nanotube Material Quality

It is well known that the raw as well as purified single wall carbon nanotube (SWCNT) material always contain certain amount of impurities of varying composition (mostly metal catalyst and non-tubular carbon). Particular purification method also creates defects and/or functional groups in the SWCNT material and therefore affects the its dispersability in solvents (important to subsequent application development). A number of analytical characterization tools have been used successfully in the past years to assess various properties of nanotube materials, but lack of standards makes it difficult to compare these measurements across the board. In this work we report the protocol developed at NASA-JSC which standardizes measurements using TEM, SEM, TGA, Raman and UV-Vis-NIR absorption techniques. Numerical measures are established for parameters such as metal content, homogeneity, thermal stability and dispersability, to allow easy comparison of SWCNT materials. We will also report on the recent progress in quantitative measurement of non-tubular carbon impurities and a possible purity standard for SWCNT materials

Low-energy quasiparticle transport through Andreev levels

We measure the resistance of a normal mesoscopic sample with two Superconducting mirrors and find two regimes with qualitatively different behavior. At temperatures below 90 mK peaks in the conductance were found when the phase difference between the two superconductors is an odd multiple of rr. The peak heights increase with decreasing temperature. Above 100 mK the observed peaks give way to dips in the conductance. While the high-temperature behavior can be explained in terms of the thermal effect [Phys. Rev. Lett, 76, 823 (1996)], we propose that the low-temperature behavior is: a manifestation of resonant transmission of low-energy quasiparticles through Andreev states. [S0163-1829(99)11641-2]

Raman mapping glucose metabolites during human mesenchymal stem cell adipogenesis

Raman mapping was used to determine the lipid distribution inside human mesenchymal stem cells during induced adipogenesis by monitoring C-H stretching bands of the fats inside the lipid droplets. By incorporating deuterated glucose into the cell culture medium during induction it was possible to distinguish whether or not downstream metabolites, either in lipid droplets or in the cytoplasm, had been formed before or after the adipogenic cascade, because C-D stretching bands are 1/√2 shifted compared to the C-H bands. Thus, metabolites formed after the initiation of the process displayed both C-H and C-D stretching bands and so were forming during induced adipogenesis rather than prior to it. With the ability to distinguish small putative lipid drops formed by the induction of adipogenesis from those pre-formed in the cell, it was possible to analyze spectral changes occurring in the droplets at the earliest stages of adipogenesis. There were two key findings. Firstly, Raman spectra of lipid droplets evolved over time, suggesting that their composition at the early stages was not the same as at the later stages. Secondly, it was apparent that the proportion of unsaturated fats in droplets was higher at early stages than it was at later stages, suggesting that unsaturated fats arrive in the droplets faster than saturated ones