dimension formula for the affine deligne lusztig variety x mu b x μ b the study of certain union x mu b of affine deligne lusztig varieties in the affine flag varieties arose from the study of shimura varieties with iwahori level structure in this paper we give an explicit dimension formula for x mu b associated to sufficiently large dominant coweight mu

character sheaves v this paper is part of a series s 131 devoted to the study of a class g of irreducible perverse sheaves called character sheaves on a connected reductive algebraic group g the numbering of chapters sections and references will continue that of s 131 this paper is a step towards the classification of character sheaves on g one of the main results is the following one under certain assumptions there is a natural surjective map with finite fibers from g to the set of all pairs 9 c up to conjugacy by the weyl group where 9 is a tame local system on the maximal torus and c is a two sided cell in the stabilizer w of 9 in the weyl group the assumptions made on g are

credal classification rule for uncertain data based on belief functions abstract in this paper we present a new credal classification rule ccr based on belief functions to deal with the uncertain data ccr allows the objects to belong with different masses of belief not only to the specific classes but also to the sets of classes called meta classes which correspond to the disjunction of several specific classes each specific class is characterized by a class center i e prototype and consists of all the objects that are sufficiently close to the center the belief of the assignment of a given object to classify with a specific class is determined from the mahalanobis distance between the object and the center of the corresponding class the meta classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes the selection of meta classes depends on the application and the context and a measure of the degree of indistinguishability between classes is introduced in this new ccr approach the objects assigned to a meta class should be close to the center of this meta class having similar distances to all the involved specific classes centers and the objects too far from the others will be considered as outliers noise ccr provides robust credal classification results with a relatively low computational burden several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this ccr method with respect to other classification methods

minimal length elements in twisted conjugacy classes of finite coxeter groups let w be a finite coxeter group and let f be an automorphism of w that leaves the set of generators of w invariant we establish certain properties of elements of minimal length in the f conjugacy classes of w that allow us to define character tables for the corresponding twisted iwahori hecke algebras these results are extensions of results obtained by geck and pfeiffer in the case where f is trivial

on the μ ordinary locus of a shimura variety abstract in this paper we study the ordinary locus of a shimura variety with parahoric level structure under the axioms in 12 we show that ordinary locus is a union of certain maximal ekedahl kottwitz oort rapoport strata introduced in 12 and we give criteria on the density of the ordinary locus

affineness of deligne lusztig varieties for minimal length elements abstract we prove that the deligne lusztig varieties associated to elements of the weyl group which are of minimal length in their twisted class are affine our proof differs from the proof of he and orlik rapoport and it is inspired by the case of regular elements which correspond to the varieties involved in broue s conjectures

the g stable pieces of the wonderful compactification let g be a connected simple algebraic group over an algebraically closed field there is a partition of the wonderful compactification of into finite many g stable pieces which was introduced by lusztig in this paper we will investigate the closure of any g stable piece in we will show that the closure is a disjoint union of some g stable pieces which was first conjectured by lusztig we will also prove the existence of cellular decomposition if the closure contains finitely many orbits

a subalgebra of 0 hecke algebra let w i be a finite coxeter group in the case where w is a weyl group berenstein and kazhdan in a berenstein d kazhdan geometric and unipotent crystals ii from unipotent bicrystals to crystal bases in quantum groups in contemp math vol 433 amer math soc providence ri 2007 pp 13 88 constructed a monoid structure on the set of all subsets of i using unipotent linear bicrystals in this paper we will generalize this result to all types of finite coxeter groups including non crystallographic types our approach is more elementary based on some combinatorics of coxeter groups moreover we will calculate this monoid structure explicitly for each type

a derivative free algorithm for inequality constrained nonlinear programming via smoothing of an ell_ infty penalty function in this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used our starting point is the possibility to transform the original constrained problem into an unconstrained or linearly constrained minimization of a nonsmooth exact penalty function this approach shows two main difficulties the first one is the nonsmoothness of this class of exact penalty functions which may cause derivative free codes to converge to nonstationary points of the problem the second one is the fact that the equivalence between stationary points of the constrained problem and those of the exact penalty function can only be stated when the penalty parameter is smaller than a threshold value which is not known a priori in this paper we propose a derivative free algorithm which overcomes the preceding difficulties and produces a sequence of points that admits a subsequence converging to a karush kuhn tucker point of the constrained problem in particular the proposed algorithm is based on a smoothing of the nondifferentiable exact penalty function and includes an updating rule which after at most a finite number of updates is able to determine a right value for the penalty parameter furthermore we present the results obtained on a real world problem concerning the estimation of parameters in an insulin glucose model of the human body

character sheaves on certain spherical varieties abstract we study a class of perverse sheaves on some spherical varieties which include the strata of the de concini procesi completion of a symmetric variety this is a generalization of the theory of parabolic character sheaves

minimal length elements of coxeter groups let w be a coxeter group and wj a finite parabolic subgroup we present here a geometric new proof of x he s result on minimal length elements of an orbit of wj which acts on w in a certain way

decomposition matrices for low rank unitary groups we study the decomposition matrices of the unipotent blocks of finite special unitary groups sun q for unitary primes larger than n up to few unknown entries we give a complete solution for n 2 10 we also prove a general result for two column partitions when divides q 1 this is achieved using projective modules coming from the adic cohomology of deligne lusztig varieties

the character sheaves on the group compactification abstract we give a definition of character sheaves on the group compactification which is equivalent to lusztig s definition in g lusztig parabolic character sheaves ii mosc math j 4 4 2004 869 896 we also prove some properties of the character sheaves on the group compactification

connected components of closed affine deligne lusztig varieties for rese fgln abstract let f be a p adic field and let e f be a finite unramified extension for the weil restriction res e f g l n of the general linear group g l n we determine the connected components of closed affine deligne lusztig varieties of arbitrary parahoric level

on the affineness of deligne lusztig varieties abstract we prove that the deligne lusztig variety associated to minimal length elements in any conjugacy class of the weyl group is affine which was conjectured by orlik and rapoport in s orlik m rapoport deligne lusztig varieties and period domains over finite fields arxiv 0705 1646

green polynomials of weyl groups elliptic pairings and the extended dirac index abstract in this paper we give a uniform construction of irreducible genuine characters of the pin cover w of a weyl group w and put them into the context of theory of springer representations in the process we provide a direct connection between springer theory via green polynomials the irreducible representations of w and an extended dirac operator for graded hecke algebras we also introduce a q elliptic pairing for w with respect to the reflection representation v these constructions are of independent interest the q elliptic pairing is a generalization of the elliptic pairing of w introduced by reeder and it is also related to s kato s notion of graded kostka systems for the semidirect product a w c w s v

centralizers of iwahori hecke algebras to date integral bases for the centre of the iwahori hecke algebra of a finite coxeter group have relied on character theoretical results and the isomorphism between the iwahori hecke algebra when semisimple and the group algebra of the finite coxeter group in this paper we generalize the minimal basis approach of f1 to provide a way of describing and calculating elements of the minimal basis for the centre of an iwahori hecke algebra which is entirely combinatorial in nature and independent of both the above mentioned theories this opens the door to further generalization of the minimal basis approach to other cases in particular we show that generalizing it to centralizers of parabolic subalgebras requires only certain properties in the coxeter group we show here that these properties hold for groups of type a and b giving us the minimal basis theory for centralizers of any parabolic subalgebra in these types of iwahori hecke algebra

minimal length elements in some double cosets of coxeter groups abstract we study the minimal length elements in some double cosets of coxeter groups and use them to study lusztig s g stable pieces and the generalization of g stable pieces introduced by lu and yakimov we also use them to study the minimal length elements in a conjugacy class of a finite coxeter group and prove a conjecture in m geck s kim g pfeiffer minimal length elements in twisted conjugacy classes of finite coxeter groups j algebra 229 2 2000 570 600

geometric and homological properties of affine deligne lusztig varieties this paper studies ane deligne lusztig varieties x w b in the ane ag variety of a quasi split tamely ramied group we describe the geometric structure of x w b for a minimal length element w in the conjugacy class of an extended ane weyl group we then provide a reduction method that relates the structure of x w b for arbitrary elements w in the extended ane weyl group to those associated with minimal length elements based on this reduction we establish a connection between the dimension of ane deligne lusztig varieties and the degree of the class polynomial of ane

lifting of elements of weyl groups abstract suppose g is a reductive algebraic group t is a cartan subgroup of g n norm t and w n t is the weyl group if w w has order d it is natural to ask about the orders lifts of w to n it is straightforward to see that the minimal order of a lift of w has order d or 2d but it can be a subtle question which holds we first consider the question of when w itself lifts to a subgroup of n in which case every element of w lifts to an element of n of the same order we then consider two natural classes of elements regular and elliptic in the latter case all lifts of w are conjugate and therefore have the same order we also consider the twisted case