Asymptotic cone of semisimple orbits for symmetric pairs

Let G be a reductive algebraic group over the complex field and O_h be a closed adjoint orbit through a semisimple element h. By a result of Borho and Kraft (1979), it is known that the asymptotic cone of the orbit O_h is the closure of a Richardson nilpotent orbit corresponding to a parabolic subgroup whose Levi component is the centralizer Z_G(h) in G. In this paper, we prove an analogue on a semisimple orbit for a symmetric pair (G, K).Comment: 14 page

Duality for nonlinear simply laced groups

Let G be a nonlinear double cover of the real points of a connected reductive complex algebraic group with simply laced root system. We establish a uniform character multiplicity duality theory for the category of Harish-Chandra modules for G.Comment: 51 pages, 1 figur

Novel P2-type Na0.6Fe0.5-2xMn0.5TixVxO2 Cathode for High-Capacity and Stable Sodium-Ion Batteries

Necessity of enery storage and battery production is soaring up steadily for the growth of portable electronic devices and surging evolution of electric vehicles and renewables. Lithium-ion battery (LIB) technology has been the primary choice for such applications due to its high-energy-density, high-stability, and longer cycle-life. Albeit with all merits, depletion of lithium reserve has prompted battery researchers to search for new alternatives to LIB. Sodium, in this respect, can be a viable solution as it is the sixth most abundant element and shares the same group with lithium in periodic table, having similar structure and electrochemical working mechanisms. The pivotal factor hindering the deployment of the laboratory-based Sodium-ion battery (SIB) technologies into the commercial battery market is low energy density compared to that of LIB. Improvement of overall electrochemical performance of cathode materials can be a game-changer as it affects energy density, lifespan, and tolerance of batteries. In this research, a novel P2-type transition metal-oxide cathode Na0.6Fe0.5-2xMn0.5TixVxO2 was synthesized by doping NaFeMnO2 (NFM) with vanadium and titanium. A set of physicochemical analyses, including Field-Effect Scanning Electron Microscopy and Energy Dispersive X-ray Spectroscopy analysis, were performed to justify the morphological competence of the pristine NFM and vanadium-titanium doped NFM and crystal structures and lattice parameters were refined through X-ray Diffraction and Rietveld analysis. These exhaustive structural and morphological comparisons provided insights on the effects of vanadium-titanium doping on stabilizing surface structures, reducing Jahn Teller distortion, enhancing stability and capacity retention, and promoting Na+ carrier transport mechanism

Characters of Springer representations on elliptic conjugacy classes

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid again on elliptic conjugacy classes) of the W-character of an irreducible discrete series representation with real central character of a graded affine Hecke algebra with arbitrary parameters. In both cases, the Pin double cover of W and the Dirac operator for graded affine Hecke algebras play key roles.Comment: 15 pages, minor changes in exposition, corrected typo