Hecke Algebra Actions on the Coinvariant Algebra

Two actions of the Hecke algebra of type A on the corresponding polynomial ring are studied. Both are deformations of the natural action of the symmetric group on polynomials, and keep symmetric functions invariant. We give an explicit description of these actions, and deduce a combinatorial formula for the resulting graded characters on the coinvariant algebra.Comment: 21 pages; final form, to appear in the Journal of Algebr

Combinatorial Gelfand Models

A combinatorial construction of a Gelafand model for the symmetric group and its Iwahori-Hecke algebra is presented.Comment: 15 pages, revised version, to appear in J. Algebr

Brownian yet non-Gaussian diffusion in heterogeneous media: from superstatistics to homogenization

We discuss the situations under which Brownian yet non-Gaussian (BnG) diffusion can be observed in the model of a particle's motion in a random landscape of diffusion coefficients slowly varying in space. Our conclusion is that such behavior is extremely unlikely in the situations when the particles, introduced into the system at random at $t=0$, are observed from the preparation of the system on. However, it indeed may arise in the case when the diffusion (as described in Ito interpretation) is observed under equilibrated conditions. This paradigmatic situation can be translated into the model of the diffusion coefficient fluctuating in time along a trajectory, i.e. into a kind of the "diffusing diffusivity" model.Comment: 12 pages; 10 figure

Natural FLRW metrics on the Lie group of nonzero quaternions

It is shown that the Lie group of invertible elements of the quaternion algebra carries a family of natural closed Friedmann-Lemaitre-Robertson-Walker metrics.Comment: A slightly more technical version of "Natural geometry of nonzero quaternions" IJTP 46 (2) (2007) 251-25

Density functional simulation of small Fe nanoparticles

We calculate from first principles the electronic structure, relaxation and magnetic moments in small Fe particles, applying the numerical local orbitals method in combination with norm-conserving pseudopotentials. The accuracy of the method in describing elastic properties and magnetic phase diagrams is tested by comparing benchmark results for different phases of crystalline iron to those obtained by an all-electron method. Our calculations for the bipyramidal Fe_5 cluster qualitatively and quantitatively confirm previous plane-wave results that predicted a non-collinear magnetic structure. For larger bcc-related (Fe_35) and fcc-related (Fe_38, Fe_43, Fe_62) particles, a larger inward relaxation of outer shells has been found in all cases, accompanied by an increase of local magnetic moments on the surface to beyond 3 mu_B.Comment: 15 pages with 6 embedded postscript figures, updated version, submitted to Eur.Phys.J.

Spectral properties of fractional Fokker-Plank operator for the L\'evy flight in a harmonic potential

We present a detailed analysis of the eigenfunctions of the Fokker-Planck operator for the L\'evy-Ornstein-Uhlenbeck process, their asymptotic behavior and recurrence relations, explicit expressions in coordinate space for the special cases of the Ornstein-Uhlenbeck process with Gaussian and with Cauchy white noise and for the transformation kernel, which maps the fractional Fokker-Planck operator of the Cauchy-Ornstein-Uhlenbeck process to the non-fractional Fokker-Planck operator of the usual Gaussian Ornstein-Uhlenbeck process. We also describe how non-spectral relaxation can be observed in bounded random variables of the L\'evy-Ornstein-Uhlenbeck process and their correlation functions.Comment: 10 pages, 5 figures, submitted to Euro. Phys. J.