Noncommutative algebras related with Schubert calculus on Coxeter groups

For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I₂(m). We define a “quantization” and a multiparameter deformation of our construction and show that for Lie groups of classical type and G₂, the algebra generated by Dunkl’s elements in the quantized bracket algebra is canonically isomorphic to the small quantum cohomology ring of the corresponding flag variety, as described by B. Kim. For crystallographic Coxeter systems we define the so-called quantum Bruhat representation of the corresponding bracket algebra. We study in more detail the structure of the relations in B_n-, D_n- and G₂-bracket algebras, and as an application, discover a Pieri-type formula in the B_n-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary B_n-Schubert class by some special ones. Our Pieri-type formula is a generalization of Pieri’s formulas obtained by A. Lascoux and M.-P. Schützenberger for flag varieties of type A. We also introduce a super-version of the bracket algebra together with a family of pairwise anticommutative elements, the so-called flat connections with constant coefficients, which describes “a noncommutative differential geometry on a finite Coxeter group” in the sense of S. Majid.     

Thermodynamic Control of Domain Swapping by Modulating the Helical Propensity in the Hinge Region of Myoglobin

Domain swapping is an exception to Anfinsen's dogma, and more than one structure can be produced from the same amino acid sequence by domain swapping. We have previously shown that myoglobin (Mb) can form a domain‐swapped dimer in which the hinge region is converted to a helical structure. In this study, we showed that domain‐swapped dimerization of Mb was achieved by a single Ala mutation of Gly at position 80. Multiple Ala mutations at positions 81 and 82 in addition to position 80 facilitated dimerization of Mb by stabilization of the dimeric states. Domain swapping tendencies correlated well with the helical propensity of the mutated residue in a series of Mb mutants with amino acids introduced to the hinge region. These findings demonstrate that a single mutation in the hinge loop to modify helical propensity can control oligomer formation, providing new ideas to create high‐order protein oligomers using domain swapping.     

Enantioselective Protonation of Cyclic Carbonyl Ylides by Chiral Lewis Acid Assisted Alcohols

Chiral Lewis acid-catalyzed asymmetric alcohol addition reactions to cyclic carbonyl ylides generated from N-(α-diazocarbonyl)-2-oxazolidinones featuring a dual catalytic system are reported. Construction of a chiral quaternary heteroatom-substituted carbon center was accomplished in which the unique heterobicycles were obtained in good yields with high stereoselection. The alcohol adducts were successfully converted to optically active oxazolidine-2,4-diones by hydrolysis. Mechanistic studies by DFT calculations revealed that alcohols could be activated by Lewis acids, enabling enantioselective protonation of the carbonyl ylides.     

Mechanism of hopping transport in disordered mott insulators

By using a combination of detailed experimental studies and simple theoretical arguments, we identify a novel mechanism characterizing the hopping transport in the Mott insulating phase of Ca2-xSrxRuO4 near the metal-insulator transition. The hopping exponent alpha shows a systematic evolution from a value of alpha=1/2 deeper in the insulator to the conventional Mott value alpha=1/3 closer to the transition. This behavior, which we argue to be a universal feature of disordered Mott systems close to the metal-insulator transition, is shown to reflect the gradual emergence of disorder-induced localized electronic states populating the Mott-Hubbard gap.     

Gap structure of the spin-triplet superconductor Sr2RuO4 determined from the field-orientation dependence of the specific heat

We report the field-orientation dependent specific heat of the spin-triplet superconductor Sr2RuO4 under the magnetic field aligned parallel to the RuO2 planes with high accuracy. Below about 0.3 K, striking fourfold oscillations of the density of states reflecting the superconducting gap structure have been resolved for the first time. We also obtained strong evidence of multiband superconductivity and concluded that the superconducting gap in the active band, responsible for the superconducting instability, is modulated with a minimum along the [100] direction.     

Fermi surface, surface states, and surface reconstruction in Sr2RuO4

The electronic structure of Sr2RuO4 is investigated by high angular resolution ARPES at several incident photon energies. We address the controversial issues of the Fermi surface (FS) topology and the van Hove singularity at the M point, showing that a surface state and the replica of the primary FS due to sqrt[2]xsqrt[2] surface reconstruction are responsible for previous conflicting interpretations. The FS thus determined by ARPES is consistent with the de Haas-van Alphen results, and it provides additional information on the detailed shape of the alpha, beta, and gamma sheets.