complexes de chaines etales et courbes de deligne lusztig abstract in a first part we lift the usual constructions of functors between derived categories of etale sheaves over schemes with a sheaf of algebras to pure derived categories for varieties with finite group actions we recover in a more functorial way rickard s construction we apply this to the case of deligne lusztig varieties and show that broue s conjecture holds for curves the additional ingredient we need is obtained from an easy property of the cohomology of etale covers of the affine line

a note on decomposition numbers for groups of lie type of small rank abstract using virtual projective characters coming from the l adic cohomology of deligne lusztig varieties we determine new decomposition numbers for principal blocks of some groups of lie type of small rank including g 2 q and steinberg s triality groups d 4 3 q

influence curves of estimators for directional data much recent research has centred on the robustness of estimators particularly estimators of location and scale for linear data however the robustness of estimators for directional data has not been investigated comprehensively mardia 1975 and discussants mentioned some aspects of robustness collett 1980 investigated outliers in circular data in this note we will use the influence curve introduced by hampel 1974 as a heuristic tool in evaluating the robustness of some estimators of location for directional data discussed by mardia 1972 similar calculations can be used to obtain influence curves for scale estimators for the location model we consider a circular distribution f which is unimodal and symmetric about the unknown direction p let p be the known concentration parameter the sample circular mean is the most commonly used measure of location we express the circular population mean in functional form as

asymptotic stability of the stationary solution to an initial boundary value problem for the mullins equation of fourth order in the present article we first study the existence of the stationary solution to an initial boundary value problem for the mullins equation of fourth order which was proposed by mullins two dimensional motion of idealized grain boundaries j appl phys 27 900 1956 to describe the groove development due to the surface diffusion at the grain boundaries of a heated polycrystal then employing an energy method we prove that this stationary solution is asymptotically stable in a suitable norm as time goes to infinity

cohomology of deligne lusztig varieties for short length regular elements in exceptional groups abstract we determine the cohomology of deligne lusztig varieties associated with some short length regular elements for split groups of type f 4 and e n as a byproduct we obtain conjectural brauer trees for the principal 14 block of e 7 and the principal 24 block of e 8

comment on on a property of a classical solution of the nonlinear mass transport equation ut uxx 1 ux2 ii j math phys 28 536 1987 a mechanism of smoothing due to evaporation condensation of the roughly perturbed surface of a solid is formulated as a cauchy problem in the real line r1 for the equation ut uxx 1 ux2 which describes the evolution of the profile u x t of the surface in the preceding paper a kitada and h umehara j math phys 28 536 1987 it was demonstrated that if the solution u x t of the cauchy problem is obtained in the classical sense with an additional restriction u c3 r1 0 each peak in the surface decreases in height with time in the strict sense in the present paper by modifying the proof it is shown that the additional restriction to the classical solution is excessive

coxeter orbits and brauer trees abstract we study the cohomology with modular coefficients of deligne lusztig varieties associated to coxeter elements under some torsion free assumption on the cohomology we derive several results on the principal l block of a finite reductive group g f q when the order of q modulo l is assumed to be the coxeter number these results include the determination of the planar embedded brauer tree of the block as conjectured by hiss lubeck and malle 1995 in 25 and the derived equivalence predicted by the geometric version of broue s conjecture broue and malle 1993 7

on the estimation of slope and the identification of outliers in linear regression summary the paper presents a large sample method for estimating the slope parameter in a linear model by minimizing a loss function related to the empirical cumulant generating function of the error distribution a family of estimators indexed by a real parameter is obtained and consistency and asymptotic normality established the optimum member of the family is that which has minimum variance with respect to the parameter this minimization together with a characterization result for the normal distribution leads to a procedure for the identification of outliers with respect to least squares

finite complex reflection arrangements are k pi 1 let v be a finite dimensional complex vector space and w gl v be a finite complex reflection group let v reg be the complement in v of the reflecting hyperplanes we prove that v reg is a k 1 space this was predicted by a classical conjecture originally stated by brieskorn for complexified real reflection groups the complexified real case follows from a theorem of deligne and after contributions by nakamura and orliksolomon only six exceptional cases remained open in addition to solving these six cases our approach is applicable to most previously known cases including complexified real groups for which we obtain a new proof based on new geometric objects we also address a number of questions about 1 w v the braid group of w this includes a description of periodic elements in terms of a braid analog of springer s theory of regular elements

an angular approach for linear data summary a procedure for estimating the slope in a linear model which was introduced by chambers heathcote 1981 is reexamined a careful analysis of the procedure leads to a geometric interpretation in terms of arngular random variables this interpretation motivates a method of estimating the location or intercept simplifies the evaluation of the robustness of the procedure and provides insight into the relationship between the method and other robust techniques

an algorithmic approach to perverse derived equivalences broue s conjecture for ω8 2 abstract following craven and rouquier s method 8 to tackle broue s abelian defect group conjecture we present two algorithms implementing that procedure in the case of principal blocks of defect d c l c l for a prime l the first describes a stable equivalence between b 0 g and b 0 n g d and the second tries to lift such a stable equivalence to a perverse derived equivalence as an application we show that broue s conjecture holds for the principal 5 block of the simple group 8 2

bahadur representations for robust scale estimators based on regression residuals on etudie le comportement asymptotique de la deviation mediane et de l etendue semi interquantile

exact solvability of the mullins nonlinear diffusion model of groove development the mullins equation for the development of a surface groove by evaporation condensation is yt yxx 1 y2x it is pointed out that this is the equation of the potential for the field variable satisfying the nonlinear diffusion equation t x x 1 2 the latter has already been solved exactly with boundary conditions corresponding exactly to those specified by mullins the depth of a groove at a grain boundary is predicted exactly without first making the linear small slope approximation for some types of initial data the cauchy problem may be solved for some related equations

normalizers of parabolic subgroups in coxeter groups we shall describe a simple procedure for obtaining presentations of normalizers of parabolic subgroups of arbitrary coxeter groups in each case the normalizer is the semidirect product of the parabolic subgroup by a complement which acts by permuting the simple re ections this complement may be viewed in a natural way as a maximal subgroup of a certain groupoid for which we obtain a set of generators and de ning relations moreover the de ning relations are all derived from subgroupoids of ranks one and two so that the groupoid can be viewed as a generalization of a coxeter group

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

brauer trees for blocks of cyclic defect in the groups g2 q for primes dividing q2 q 1 1 are dealt with in sl 1 where we also describe the blocks of noncyclic defect for these primes these results form part of a project proposed by walter feit namely to determine the brauer trees for all finite groups the blocks and brauer trees for the groups g 2k and g2 3k are described in s2 and a survey of all the results in this paper and in sl sz is given in s3 the conjugacy classes and character tables for

cohomological goodness and the profinite completion of bianchi groups the concept of cohomological goodness was introduced by j p serre in his book on galois cohomology 31 this property relates the cohomology groups of a group to those of its profinite completion we develop properties of goodness and establish goodness for certain important groups we prove for example that the bianchi groups i e the groups psl 2 o where o is the ring of integers in an imaginary quadratic number field are good as an application of our improved understanding of goodness we are able to show that certain natural central extensions of fuchsian groups are residually finite this result contrasts with examples of p deligne 5 who shows that the analogous central extensions of sp 4 z do not have this property

existence and long time behaviour of weak solutions for the mullins equation abstract we study the initial boundary value problem for the fourth order mullins equation with initial data h 0 w 1 1 under an assumption that the specific free energy of the boundary is less than the surface free energy the model that we study was derived by mullins in 1957 to analyse the time evolution of surface grooves at the grain boundaries of heated polycrystal we prove global in time existence of weak solutions and we also show that the energy minimizing steady state is the global attractor

perverse equivalences and broueʼs conjecture abstract we give a new approach to the construction of derived equivalences between blocks of finite groups based on perverse equivalences in the setting of broue s abelian defect group conjecture we provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with sylow subgroups elementary abelian of order 9 we also examine extensions to automorphism groups in a general setting

parabolic deligne lusztig varieties abstract motivated by the broue conjecture on blocks with abelian defect groups for finite reductive groups we study parabolic deligne lusztig varieties and construct on those which occur in the broue conjecture an action of a braid monoid whose action on their l adic cohomology will conjecturally factor through a cyclotomic hecke algebra in order to construct this action we need to enlarge the set of varieties we consider to varieties attached to a ribbon category this category has a garside family which plays an important role in our constructions so we devote the first part of our paper to the necessary background on categories with garside families

a rapid proof for a flattening property of a classical solution of the mullins equation modifying previous proof based on the maximum principles j math phys 27 1391 1986 28 536 2982 1987 a rapid proof is proposed for a flattening property of a classical solution of the cauchy problem associated with the mullins equation ut uxx 1 ux2 x t r1 0 u x 0 x x r1 which describes the development of material surface due to evaporation condensation