on decomposition matrices for graded algebras abstract we study the relations between the decomposition matrix of a module over a graded algebra and the decomposition matrix of its restriction to the grading subalgebra we show that under appropriate hypotheses if one of the decomposition matrices is stable unitriangular then so is the other a particular case is when one of them is square unitriangular then both are using these results we describe the decomposition matrices of the hecke algebras of the complex reflection groups g de e n with respect to the ones of the ariki koike algebras or the decomposition matrices of q schur algebras of type dn with respect to the ones of q schur algebras of type bn

blocks of cyclotomic hecke algebras abstract this paper classifies the blocks of the cyclotomic hecke algebras of type g r 1 n over an arbitrary field rather than working with the hecke algebras directly we work instead with the cyclotomic schur algebras the advantage of these algebras is that the cyclotomic jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic schur algebras we obtain an explicit description of the blocks by analyzing the combinatorics of jantzen equivalence we remark that a proof of the classification of the blocks of the cyclotomic hecke algebras was announced in 1999 unfortunately cox has discovered that this previous proof is incomplete

anomalous roughening in three dimensional polynucleation growth abstract the surface properties of the three dimensional polynucleation growth model were studied at the kinetic roughening transition the dependence of the surface width w on time t and linear size l of the substrate is determined by anomalous roughening w x log l tf t l z where tf is a scaling function for the exponents x 2 8 0 2 and z 1 79 0 05 were found the latter being related to directed percolation

representation theory of a hecke algebra of g r p n abstract in our previous paper 1 we introduced a notion of a hecke algebra for a series of complex reflection groups z r z k n which is the group of n by n permutation matrices with entries running through rth roots of unity the ordinary representation of the algebra is also studied in it the results are direct generalizations of hoefsmit s 4 for hecke algebras of classical weyl groups in this paper we establish a similar theory for the remaining series of complex reflection groups g r p n p r p 1 is the case we previously considered in 1 the construction of the hecke algebra was soon generalized to the case p 2 by broue and malle 2 motivated by a much deeper background in 2 they conjectured that these hecke algebras over a ring of l adic integers are candidates for endomorphism rings of certain deligne lusztig modules over the ring which arise in modular representation theory related to algebraic groups they also defined hecke algebras of complex reflection groups for not all but various kinds of exceptional and two dimensional cases in the same context the first section starts with the definition of the hecke algebra and then we prove that they actually have desirable properties the second section is for explicit construction of irreducible representations we call them the representations of semi normal form the author deeply thanks professor broue and professor malle since he was able to learn much from them and they hinted him to the problem

numerical integration of stochastic differential equations several numerical methods for treating stochastic differential equations are considered both the convergence in the mean square limit and the convergence of the moments is discussed and the generation of appropriate random numbers is treated the necessity of simulations at various time steps with an extrapolation to time step zero is emphasized and demonstrated by a simple example

modular representations of hecke algebras of type g p p n hecke algebras for the complex reflection groups g r p n where p 1 and p r were introduced in the work of ariki j algebra 177 1995 164 185 broue and malle asterisque 212 1993 119 189 in this paper we consider modular representation theory for these algebras in the case where r p we assume that the field k contains a primitive pth root of unity e our method is to study the restrictions of specht modules s for hecke algebras hp n of type g p 1 n with parameters q 1 e ep 1 suppose that f q e 0 in k see 4 7 for definition of f q e for any multipartition 1 p of n we prove that s hp p n s k hp p n for any 1 k p 1 where k k 1 k 2 p 1 2 k and if k is the smallest positive integer such that k hence k p we explicitly decompose s hp p n into a direct sum of p k smaller hp p n submodules with the same dimensions as a result when f q e 0 in k we show that hp p n is split over k and get a complete classification of all the absolutely irreducible hp p n modules this generalizes earlier work of c pallikaros j algebra 169 1994 20 48 and j hu manuscripta math 108 2002 409 430 on hecke algebras of type dn which are included as a special case of our main results

vectorized and parallel simulations of the kardar parisi zhang equation in 3 1 dimensions the kardar parisi zhang kpz equation describing kinetic roughening is solved numerically for 3 1 dimensional systems in the strong coupling phase by massive use of supercomputing tools we calculate for the first time the exponent beta 0 181 or 0 007 with an accuracy comparable with that of lattice growth model simulations a possible source of errors in parallel monte carlo calculations is pointed out

on the decomposition numbers of the hecke algebra of type dn when n is even abstract let n 4 be an even integer let k be a field with char k 2 and q an invertible element in k such that i 1 n 1 1 q i 0 in this paper we study the decomposition numbers over k of the iwahori hecke algebra h q d n of type d n we obtain some equalities which relate its decomposition numbers with certain schur elements and the decomposition numbers of various iwahori hecke algebras of type a with the same parameter q when char k 0 this completely determine all of its decomposition numbers the main tools we used are the morita equivalence theorem established in j hu a morita equivalence theorem for hecke algebra h q d n when n is even manuscripta math 108 2002 409 430 and certain twining character formulae of weyl modules over a tensor product of two q schur algebras

dynamics of driven interfaces near isotropic percolation transition we consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold in particular we study simple discrete forest fire lattice models through monte carlo simulations in two and three spatial dimensions an interface generated in the models is found to display complex behavior away from the percolation transition the interface is self affine with asymptotic dynamics consistent with the kardar parisi zhang universality class however in the vicinity of the percolation transition there is a different behavior at earlier times by scaling arguments we show that the global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying percolation cluster our numerical results are in good agreement with theory however we demonstrate that at the depinning transition the interface as defined in the models is no longer self affine finally we compare these results with those obtained from a more realistic reaction diffusion model of slow combustion s1063 651x 98 08708 x

airy distribution function from the area under a brownian excursion to the maximal height of fluctuating interfaces the airy distribution function describes the probability distribution of the area under a brownian excursion over a unit interval surprisingly this function has appeared in a number of seemingly unrelated problems mostly in computer science and graph theory in this paper we show that this distribution function also appears in a rather well studied physical system namely the fluctuating interfaces we present an exact solution for the distribution p h m l of the maximal height h m measured with respect to the average spatial height in the steady state of a fluctuating interface in a one dimensional system of size l with both periodic and free boundary conditions for the periodic case we show that p h m l l 1 2f h m l 1 2 for all l 0 where the function f x is the airy distribution function this result is valid for both the edwards wilkinson ew and the kardar parisi zhang interfaces for the free boundary case the same scaling holds p h m l l 1 2f h m l 1 2 but the scaling function f x is different from that of the periodic case we compute this scaling function explicitly for the ew interface and call it the f airy distribution function numerical simulations are in excellent agreement with our analytical results our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables some of these results were announced in a recent letter s n majumdar and a comtet phys rev lett 92 225501 2004

the jantzen sum formula for cyclotomic schur algebras the cyclotomic q schur algebra was introduced by dipper james and mathas in order to provide a new tool for studying the ariki koike algebra we here prove an analogue of jantzen s sum formula for the cyclotomic q schur algebra among the applications is a criterion for certain specht modules of the ariki koike algebras to be irreducible

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

anisotropic percolation and the d dimensional surface roughening problem we review recent numerical simulations of several models of interface growth in ddimensional media with quenched disorder these models belong to the universality class of anisotropic diode resistor percolation networks the values of the roughness exponent y 0 63 0 01 d 1 1 and y 0 48 2 0 02 d 2 1 are in good agreement with our recent experiments the values of y in higher dimensions a 0 38 5 0 03 in d 4 and y 0 27 0 05 in d 5 do not support a recent theoretical conjecture

morita equivalences of ariki koike algebras we prove that every ariki koike algebra is morita equivalent to a direct sum of tensor products of smaller ariki koike algebras which have q connected parameter sets a similar result is proved for the cyclotomic q schur algebras combining our results with work of ariki and uglov the decomposition numbers for the ariki koike algebras defined over fields of characteristic zero are now known in principle

scaling properties of eden clusters in three and four dimensions we study the scaling properties of noise reduced eden clusters in three and four dimensions for variant b in the strip geometry we find that the width w for large times behaves as a s g lsd 1 where l is the width of the strip s the noise reduction parameter d the dimension of space and a s a decreasing function of s g is a scaling function with the property g u 12 as u 0 and g u ux as u where is the roughness exponent this scaling result leads to a new way of determining in 3 dimensions our numerical values for support a recent conjecture by kim and kosterlitz 2 d 2 and contradict all the former analytical conjectures in 4 dimensions we cannot distinguish between the conjectures of kim and kosterlitz and the conjecture of wolf and kertesz because large crossovers and finite size effects make the measurement of the exponents difficult

robin type boundary conditions in transition from reaction diffusion equations in 3d domains to equations in 2d domains abstract we consider a singular limit of diffusion equations in 3d domains of thickness converging to zero in the 2d limit the resulting reaction diffusion equation has a source term resulting from the robin type boundary conditions imposed on boundaries of the original 3d domain the proposed approach can be applied to constructing approximate solutions of diffusion problems in thin planar cylindrical or spherical layers between two membranes as an example we refer to the problem of activation of b lymphocytes which typically have large nuclei and a thin cytoplasmic layer which can be considered as a spherical shell for this example assuming additionally axial symmetry we provide a rigorous convergence theorem in the language of semigroups of operators

maximal and minimal height distributions of fluctuating interfaces maximal and minimal height distributions mahd mihd of two dimensional interfaces grown with the nonlinear equations of kardar parisi zhang kpz second order and of villain lai das sarma vlds fourth order are shown to be different two universal curves may be mahd or mihd of each class depending on the sign of the relevant nonlinear term which is confirmed by results of several lattice models in the kpz and vlds classes the difference between mahd and midh is connected with the asymmetry of the local height distribution a simple exactly solvable deposition erosion model is introduced to illustrate this feature the average extremal heights scale with the same exponent of the average roughness in contrast to other correlated systems generalized gumbel distributions do not fit those mahd and mihd nor those of edwards wilkinson growth

multisurface coding simulations of the restricted solid on solid model in four dimensions we study the restricted solid on solid model for surface growth in spatial dimension d 4 by means of a multisurface coding technique that allows us to analyze samples of size up to 256 4 in the steady state regime for such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations a careful finite size scaling analysis of the critical exponents clearly indicate that d 4 is not the upper critical dimension of the model

crossover and finite size effects in the 1 1 dimensional kardar parisi zhang equation crossover scaling of the surface width in the kardar parisi zhang equation for surface growth is studied numerically by means of a perturbative solution of the discretized equation and by comparison with the exact solution of the corresponding linear equation the finite size effects due to the spatial discretization are carefully analyzed the dependence on the nonlinearity of both the finite size and asymptotic scaling forms is then investigated

strong coupling behaviour in discrete kardar parisi zhang equations we present a systematic discretization scheme for the kardar parisi zhang kpz equation which correctly captures the strong coupling properties of the continuum model in particular we show that the scheme contains no finite time singularities in contrast to conventional schemes the implications of these results to i previous numerical integration of the kpz equation and ii the non trivial diversity of universality classes for discrete models of kpz type are examined the new scheme makes the strong coupling physics of the kpz equation more transparent than the original continuum version and allows the possibility of building new continuum models which may be easier to analyse in the strong coupling regime

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

numerical solution of the kardar parisi zhang equation in one two and three dimensions abstract on a course grained level a family of microscopic growth processes may be described by a stochastic differential equation which is solved numerically for surface dimensions d 1 2 and 3 dimensional analysis shows that the spatial discretization parameter has the meaning of an effective coupling constant the numerical stability of the euler integration scheme is discussed for the strong coupling exponents defined by surface width time the following effective values were obtained d 1 0 330 0 004 and d 2 0 24 0 005 considering the width and its ensemble fluctuations at constant dimensionless time the transition between strong and weak coupling phases is located in d 3 for the largest coupling for which reliable data are available we obtain an effective exponent close to the best estimates on discrete models d 3 0 17