An interpretation of the tame local Langlands correspondence for <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">PGSp</Emphasis>(4) from the perspective of real groups

Let F be a p-adic field. In this paper, we continue the work of the first author and give a new realization of the tame local Langlands correspondence for PGSp(4, F) that is analogous to the construction of the local Langlands correspondence for real groups.     

Simplicity of vacuum modules over affine Lie superalgebras

We prove an explicit condition on the level k for the irreducibility of a vacuum module $V^k$ over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the simplicity conditions for the corresponding minimal W-algebras obtained via quantum reduction, in all cases except when the level k is a non-negative integer.     

Electronic structure of binuclear mixed valence copper azacryptates derived from integrated advanced EPR and DFT calculations

Binuclear, mixed valence copper complexes with a [Cu(+1)(.5), Cu(+1)(.5)] redox state and S = (1)/(2) can be stabilized with rigid azacryptand ligands. In this system the unpaired electron is delocalized equally over the two copper ions, and it is one of the very few synthetic models for the electron mediating Cu(A) site of nitrous oxide reductase and cytochrome c oxidase. The spatial and electronic structures of the copper complex in frozen solution were obtained from the magnetic interactions, namely the g-tensor and the (63,65)Cu, (14)N, (2)H, and (1)H hyperfine couplings, in combination with density functional theory (DFT) calculations. The magnetic interactions were determined from continuous wave (CW) electron paramagnetic resonance (EPR), pulsed electron nuclear double resonance (ENDOR), two-dimensional TRIPLE, and hyperfine sublevel correlation spectroscopy (HYSCORE) carried out at W-band or/and X-band frequencies. The DFT calculated g and Cu hyperfine values were in good agreement with the experimental values showing that the structure in solution is indeed close to that of the optimized structure. Then, the DFT calculated hyperfine parameters were used as guidelines and starting points in the simulations of the various experimental ENDOR spectra. A satisfactory agreement with the experimental results was obtained for the (14)N hyperfine and quadrupole interactions. For (1)H the DFT calculations gave good predictions for the hyperfine tensor orientations and signs, and they were also successful in reproducing trends in the magnitude of the various proton hyperfine couplings. These, in turn, were very useful for ENDOR signals assignments and served as constraints on the simulation parameters.     

Hecke Algebras and Automorphic Forms

The goal of this paper is to carry out some explicit calculations of the actions of Hecke operators on spaces of algebraic modular forms on certain simple groups. In order to do this, we give the coset decomposition for the supports of these operators. We present the results of our calculations along with interpretations concerning the lifting of forms. The data we have obtained is of interest both from the point of view of number theory and of representation theory. For example, our data, together with a conjecture of Gross, predicts the existence of a Galois extension of Q with Galois group G ₂(F₅) which is ramified only at the prime 5. We also provide evidence of the existence of the symmetric cube lifting from PGL₂ to PGSp₄.     

Combinatorial Synthesis of Small Organic Molecules

Combinatorial synthesis has developed within a few years from a laboratory curiosity to a method that is taken seriously in drug research. Rapid progress in molecular biology and the resulting ability to determine the activity of new substances extremely efficiently have led to a change in paradigm for the synthesis of test compounds: in addition to the conventional procedure of synthesizing one substance after another, new methods allowing simultaneous creation of many structurally defined substances are becoming increasingly important. A characteristic of combinatorial synthesis is that a reaction is performed with many synthetic building blocks at once—in parallel or in a mixture— rather than with just one building block. All possible combinations are formed in each step, so that a large number of products, a so-called library, is obtained from only a few reactants. Several methods have been developed for combinatorial synthesis of small organic molecules, based on research into peptide library synthesis: single substances are produced by highly automated parallel syntheses, and special techniques enable targeted synthesis of mixtures with defined components. Many structures can be obtained by combinatorial synthesis, and the size of the libraries created ranges from a few individual compounds to many thousand substances in mixtures. This article gives an overview of the combinatorial syntheses of small organic molecules reported to date, performed both in solution and on a solid support. In addition, different techniques for identification of active compounds in mixtures are presented, together with ways to automate syntheses and process the large amounts of data produced. An overview of pionering companies active in this area is also given. The final outlook attempts to predict the future development of this exponentially growing area and the influence of this new thinking in other areas of chemistry.     

Synthesis, characterization, and physicochemical properties of manganese(III) and manganese(V)-oxo corrolazines

The structural and physicochemical properties of the manganese-corrolazine (Cz) complexes (TBP8Cz)Mn(V)O (1) and (TBP8Cz)Mn(III) (2) (TBP = p-tert-butylphenyl) have been determined. Recrystallization of 2 from toluene/MeOH resulted in the crystal structure of (TBP8Cz)Mn(III)(CH3OH) (2 x MeOH). The packing diagram of 2 x MeOH reveals hydrogen bonds between MeOH axial ligands and meso N atoms of adjacent molecules. Solution binding studies of 2 with different axial ligands (Cl-, Et3PO, and Ph3PO) reveal strong binding, corroborating the preference of the Mn(III) ion for a five-coordinate environment. High-frequency and field electron paramagnetic resonance (HFEPR) spectroscopy of solid 2 x MeOH shows that 2 x MeOH is best described as a high-spin (S = 2) Mn(III) complex with zero-field splitting parameters typical of corroles. Structural information on 1 was obtained through an X-ray absorption near-edge structure (XANES)/extended X-ray absorption fine structure (EXAFS) study and compared to XANES/EXAFS data for 2 x MeOH. The XANES data for 1 shows an intense pre-edge transition characteristic of a high-valent metal-oxo species, and a best fit of the EXAFS data gives a short Mn-O bond distance of 1.56 A, confirming the structure of the metal-oxo unit in 1. Detailed spectroelectrochemical studies of 1 and 2 were performed revealing multiple reversible redox processes for both complexes, including a relatively low potential for the Mn(V) --> Mn(IV) process in 1 (near 0.0 V vs saturated calomel reference electrode). Chemical reduction of 1 results in the formation of a Mn(III)Mn(IV)(mu-O) dimer as characterized by electron paramagnetic resonance spectroscopy.