standard young tableaux in the weyl group setting abstract a generalization of the notion of standard young tableau has recently arisen from work on the representation theory of affine hecke algebras in the generalized setting a standard tableau is defined to be any element of a finite weyl group whose inversion set satisfies a certain pair of intersection conditions in this paper we prove that the set of generalized standard tableaux of fixed shape when nonempty is a certain interval in the weak ordering in addition we establish a nonemptiness criterion for the set of standard tableaux of prescribed shape these results are obtained for shapes that satisfy an integrality condition

on polynomials interpolating between the stationary state of a o n model and a q h e ground state we obtain a family of polynomials defined by vanishing conditions and associated to tangles we study more specifically the case where they are related to a o n loop model we conjecture that their specializations at zi 1 are positive in n at n 1 they coincide with the razumov stroganov integers counting alternating sign matrices

the bethe ansatz as a matrix product ansatz the bethe ansatz in its several formulations is a common tool for the exact solution of one dimensional quantum hamiltonians this ansatz asserts that several eigenfunctions of the hamiltonians are given in terms of a sum of permutations of plane waves we present results that induce us to expect that alternatively the eigenfunctions of all the exact integrable quantum chains can also be expressed by a matrix product ansatz in this ansatz several components of the eigenfunctions are obtained through the algebraic properties of properly defined matrices this ansatz allows an unified formulation of several exact integrable hamiltonians we show how to formulate this ansatz for a large family of quantum chains such as the anisotropic heisenberg model fateev zamolodchikov model izergin korepin model sutherland model t j model hubbard model etc

canonical bases for the quantum group of type a_r and piecewise linear combinatorics this work was motivated by the following two problems from the classical representation theory both problems make sense for an arbitrary complex semisimple lie algebra but since we shall deal only with the ar case we formulate them in this generality 1 construct a good basis in every irreducible finite dimensional slr 1 module v which materializes the littlewood richardson rule a precise formulation of this problem was given in 3 we shall explain it in more detail a bit later 2 construct a basis in every polynomial representation of glr 1 such that the maximal element w0 of the weyl group sr 1 considered as an element of glr 1 acts on this basis by a permutation up to a sign and explicitly compute this permutation this problem is motivated by recent work by john stembridge 10 and was brought to our attention by his talk at the jerusalem combinatorics conference may 1993

conjectures and results about parabolic induction of representations of text gl _n f in 1980 zelevinsky introduced certain commuting varieties whose irreducible components classify complex irreducible representations of the general linear group over a non archimedean local field with a given supercuspidal support we formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction the conditions are in the spirit of the geiss leclerc schroer condition that occurs in the conjectural characterization of square irreducible representations we verify some special cases of the new conjecture and check that the geometric and representation theoretic conditions are compatible in various ways

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

classification of three state hamiltonians solvable by the coordinate bethe ansatz we classify all hamiltonians with rank 1 symmetry and nearest neighbour interactions acting on a periodic three state spin chain and solvable through generalization of the coordinate bethe ansatz cba in this way we obtain four multi parametric extensions of the known 19 vertex hamiltonians such as zamolodchikov fateev izergin korepin and bariev hamiltonians apart from the 19 vertex hamiltonians there exist 17 vertex and 14 vertex hamiltonians that cannot be viewed as subcases of the 19 vertex ones in the case of 17 vertex hamiltonians we get a generalization of the genus 5 special branch found by martins plus three new ones we also get two 14 vertex hamiltonians we solve all these hamiltonians using cba and provide their spectrum eigenfunctions and bethe equations special attention is given to provide the specifications of our multi parametric hamiltonians that give back known hamiltonians

pfhc a clustering algorithm based on data partitioning for unevenly distributed datasets recently many researchers exert their effort on clustering as a primary data mining method for knowledge discovery but only few of them have focused on uneven dataset in the last research we proposed an efficient hierarchical algorithm based on fuzzy graph connectedness fhc to discover clusters with arbitrary shapes in this paper we present a novel clustering algorithm for uneven dataset pfhc which is an extended version based on fhc in pfhc dataset is divided into several local spaces firstly according to the data density of distribution where the data density in any local space is nearly uniform in order to achieve the goal local and l are used in each local domain to acquire local clustering result by fhc then boundary between local areas needs being taken into consideration for combination finally local clusters need to be merged to obtain global clusters as an extension of fhc pfhc can deal with uneven datasets more effectively and efficiently and generate better quality clusters than other methods as experiment shows furthermore pfhc is found to be able to process incremental data as well in this work

on the critical behaviour of the anisotropic biquadratic spin 1 chain a study is made of the anisotropic biquadratic spin 1 hamiltonian introduced by batchelor et al 1990 this model can be represented as a sum of operators satisfying a temperley lieb algebra its critical behaviour is explored by using the relations between mass gap amplitudes and critical exponents predicted by conformal invariance the model like in the xxz chain is found to exhibit a line of continuously varying exponents by comparing its eigenspectrum with that of the xxz hamiltonian several exact values are predicted

geometric lifting of the canonical basis and semitoric degenerations of richardson varieties in the sl n case a berenstein and a zelevinsky studied the schutzenberger involution in terms of lusztig s canonical basis 3 we generalize their construction and formulas for any semisimple lie algebra we use for this the geometric lifting of the canonical basis on which an analogue of the schutzenberger involution can be given as an application we construct semitoric degenerations of richardson varieties following a method of p caldero 6

generalized quotients in coxeter groups for w s a coxeter group we study sets of the form w v w e w i l wv 1 w i v for all v e v where v c w such sets w v here called generalized quotients are shown to have much of the rich combinatorial structure under bruhat order that has previously been known only for the case when v c s i e for minimal coset representatives modulo a parabolic subgroup we show that bruhat intervals in w v for general v c w are lexicographically shellable the mobius function on w v under bruhat order takes values in 1 0 1 for finite groups w generalized quotients are the same thing as lower intervals in the weak order this is however in general not true connections with the weak order are explored and it is shown that w v is always a complete meet semilattice and a convex order ideal as a subset of w under weak order descent classes di w e w il1 ws 1 w xt s e i for all s e s i c s are also analyzed using generalized quotients it is shown that each descent class as a poset under bruhat order or weak order is isomorphic to a generalized quotient under the corresponding ordering the latter half of the paper is devoted to the symmetric group and to the study of some specific examples of generalized quotients which arise in combinatorics for instance the set of standard young tableaux of a fixed shape or the set of linear extensions of a rooted forest suitably interpreted form generalized quotients we prove a factorization result for the quotients that come from rooted forests which shows that algebraically these quotients behave as a system of minimal coset representatives of a subset which is in general not a subgroup we also study the rank generating function for certain quotients in the symmetric group

a hierarchical clustering algorithm based on fuzzy graph connectedness many clustering methods have been proposed in the area of data mining but only few of them focused on the incremental databases in this paper an algorithm for hierarchical clustering based on fuzzy graph connectedness algorithm fhc is investigated the presented algorithm applies fuzzy set theory to hierarchical clustering method so as to discover clusters with arbitrary shape it first partitions the data sets into several sub clusters using a partitioning method and then constructs a fuzzy graph of sub clusters by analyzing the fuzzy connectedness degree among sub clusters by computing the cut graph the connected components of the fuzzy graph can be obtained hence resulting the desired clustering the algorithm can be performed in high dimensional data sets finding clusters of arbitrary shapes such as the spherical linear elongated or concave ones also rendered in this research is the incremental algorithm ifhc applicable to periodically incremental environments not only can fhc and ifhc handle data with numerical attributes but categorical attributes can be dealt with as well the results of our experimental study for data sets with arbitrary shape and size are very encouraging the experimental study in web log files is also conducted that can help discover the user access patterns efficiently the investigation demonstrates that the proposed method generates better quality clusters than traditional algorithms and scales up well for large databases

weyl group multiple dirichlet series eisenstein series and crystal bases we show that the whittaker coecients of borel eisenstein series on the metaplectic covers of glr 1 can be described as multiple dirichlet series in r complex variables whose coecients are computed by attaching a number theoretic quantity a product of gauss sums to each vertex in a crystal graph these gauss sums depend on string data previously introduced in work of lusztig berenstein and zelevinsky and littelmann these data are the lengths of segments in a path from the given vertex to the vertex of lowest weight depending on a factorization of the long weyl group element into simple reections the coecients may also be described as sums over strict gelfand tsetlin patterns the description is uniform in the degree of the metaplectic cover

a new unsupervised approach for fuzzy clustering in this paper a new level based hierarchical approach to the fuzzy clustering problem for spatial data is proposed in this approach each point of the initial set is handled as a fuzzy point of the multidimensional space fuzzy point conical form fuzzy neighbor points fuzzy joint points are defined and their properties are explored it is known that in classical fuzzy clustering the matter of fuzziness is usually a possibility of membership of each element into different classes with different positive degrees from 0 1 in this study the fuzziness of clustering is evaluated as how much in detail the properties of classified elements are investigated in this extent a new fuzzy joint points fjp method which is robust through noises is proposed algorithm of fjp method is developed and some properties of the algorithm are explored also sufficient condition to recognize a hidden optimal structure of clusters is proven the main advantage of the fjp algorithm is that it combines determination of initial clusters cluster validity and direct clustering which are the fundamental stages of a clustering process it is possible to handle the fuzzy properties with various level degrees of details and to recognize individual outlier elements as independent classes by the fjp method this method could be important in biological medical geographical information mapping etc problems

affine hecke algebras and generalized standard young tableaux abstract this paper introduces calibrated representations for affine hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations the primary technique is to provide indexing sets for controlling the weight space structure of finite dimensional modules for the affine hecke algebra using these indexing sets we show that 1 irreducible calibrated representations are indexed by skew local regions 2 the dimension of an irreducible calibrated representation is the number of chambers in the local region 3 each irreducible calibrated representation is constructed explicitly by formulas which describe the action of the generators of the affine hecke algebra on a specific basis in the representation space the indexing sets for weight spaces are generalizations of standard young tableaux and the construction of the irreducible calibrated affine hecke algebra modules is a generalization of a young s seminormal construction of the irreducible representations of the symmetric group in this sense young s construction has been generalized to arbitrary lie type

a classification of the representations of reductive algebraic groups which admit only a finite number of orbits introduction let p g gl v be a finite dimensional rational representation of a semi simple algebraic group g all defined over c then we have p pi epe and v v1i d ve where pi is an irreducible representation of g on vi for i 1 f let p be the action of g gl 1 i x g on v which is the composition of p and scalar multiplications gl 1 ion each irreducible component vi i 1 f in this paper we shall classify all the triplet g p v such that v decomposes into a finite union of g orbits prof v g kac 3 4 and the first author 7 14 but only the necessary conditions are written in 14 have already completed independently the case when p is irreducible i e f 1 prof v g kac has also completed the case when each irreducible components are gl n x gl m al al v n v m see 5 which is the development of the results of prof p gabriel 1 note that if v decomposes into the finite union of g orbits then one of the orbits must be zariski dense and hence g p v must be a prehomogeneous vector space abbrev p v we call such a p v a finite prehomogeneous vector space abbrev f p this paper consists of the following sections

hyperplane arrangements interval orders and trees abstract a hyperplane arrangement is a finite set of hyperplanes in a real affine space an especially important arrangement is the braid arrangement which is the set of all hyperplanes xi xj 1 1 i j n in rn some combinatorial properties of certain deformations of the braid arrangement are surveyed in particular there are unexpected connections with the theory of interval orders and with the enumeration of trees for instance the number of labeled interval orders that can be obtained from n intervals i1 in of generic lengths is counted there is also discussed an arrangement due to n linial whose number of regions is the number of alternating or intransitive trees as defined by gelfand graev and postnikov gelfand i m graev m i and postnikov a 1995 preprint finally a refinement is given related to counting labeled trees by number of inversions of a result of shi shi j y 1986 lecture notes in mathematics no 1179 springer verlag that a certain deformation of the braid arrangement has n 1 n 1 regions

pairs of commuting nilpotent matrices and hilbert function abstract let k be an infinite field there has been recent study of the family h n k of pairs of commuting nilpotent n n matrices relating this family to the fibre h n of the punctual hilbert scheme a n hilb n a 2 over the point np of the symmetric product sym n a 2 where p is a point of the affine plane a 2 v baranovsky the variety of pairs of commuting nilpotent matrices is irreducible transform groups 6 1 2001 3 8 r basili on the irreducibility of commuting varieties of nilpotent matrices j algebra 268 1 2003 56 80 a premet nilpotent commuting varieties of reductive lie algebras invent math 154 3 2003 653 683 in this study a pair of commuting nilpotent matrices a b is related to an artinian algebra k a b there has also been substantial study of the stratification of the local punctual hilbert scheme h n by the hilbert function as j briancon description de hilb n c x y invent math 41 1 1977 45 89 and others however these studies have been hitherto separate we first determine the stable partitions i e those for which p itself is the partition q p of a generic nilpotent element of the centralizer of the jordan nilpotent matrix j p we then explore the relation between h n k and its stratification by the hilbert function of k a b suppose that dim k k a b n and that k is algebraically closed of characteristic 0 or large enough p we show that a generic element of the pencil a b k has jordan partition the maximum partition p h whose diagonal lengths are the hilbert function h of k a b

on incidence between strata of the hilbert scheme of points on p 2 the hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated hilbert series in general the precise inclusion relation between the closures of the strata is still unknown guerimand ph d thesis universite de nice 2002 studied this problem for strata whose hilbert series are as close as possible preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata in this paper we present a new approach based on deformation theory to guerimand s result this allows us to show that the technical condition is not necessary

new exact integrable spin 1 quantum chains new exactly integrable quantum spin 1 chains are derived these new quantum hamiltonians like the xxz chain have a free parameter anisotropy and commute with the z component of the total magnetization the eigenvalues and eigenvectors are obtained directly by imposing a generalized coordinate bethe ansatz the derived bethe ansatz equations have an unusual form and the associated r matrix has a dependence with the spectral parameter that is not of difference form like the hubbard quantum chain

on the signature character of representations of p adic general linear groups in this article we calculate the signature character of certain hermitian representations of gln f for a p adic field f we further give a conjectural description for the signature character of unramified representations in terms of kostka numbers

generalized weighted conditional fuzzy clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method is one of the most popular clustering methods based on minimization of a criterion function among many existing modifications of this method conditional or context dependent c means is the most interesting one in this method data vectors are clustered under conditions based on linguistic terms represented by fuzzy sets this paper introduces a family of generalized weighted conditional fuzzy c means clustering algorithms this family include both the well known fuzzy c means method and the conditional fuzzy c means method performance of the new clustering algorithm is experimentally compared with fuzzy c means using synthetic data with outliers and the box jenkins database

decorated star triangle relations and exact integrability of the one dimensional hubbard model the exact integrability of the one dimensional hubbard model is demonstrated with the help of a novel set of triangle relations the decorated star triangle relations the covering two dimensional statistical mechanical model obeys the star triangle or yang baxter relation a conjecture is presented for the eigenvalues of the transfer matrix

on weighting clustering recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering it basically consists of penalizing solutions via weights on the instance points somehow making clustering move toward the hardest points to cluster the motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms however interest in this analogy has so far been mainly borne out from experimental studies only this paper is to the best of our knowledge the first attempt at its formalization more precisely we handle clustering as a constrained minimization of a bregman divergence weight modifications rely on the local variations of the expected complete log likelihoods theoretical results show benefits resembling those of boosting algorithms and bring modified weighted versions of clustering algorithms such as k means fuzzy c means expectation maximization em and k harmonic means experiments are provided for all these algorithms with a readily available code they display the advantages that subtle data reweighting may bring to clustering

a decomposition of solomon s descent algebra abstract a descent class in the symmetric group sn is the collection of permutations with a given descent set it was shown by l solomon j algebra41 1976 255 264 that the product in the group algebra q sn of two descent classes is a linear combination of descent classes thus descent classes generate a subalgebra of q sn we refer to it here as solomon s descent algebra and denote it by n this algebra is not semisimple but it has a faithul representation in terms of upper triangular matrices the main goal of this paper is a decomposition of its multiplicative structure it develops that n acts in a natural way on the so called lie monomials this action has a purely combinatorial description and is a crucial tool in the construction of a complete set of indecomposable representations of n in particular we obtain a natural basis of irreducible orthogonal idempotents indexed by partitions of n for the quotient n n natural bases of nilpotents and idempotents for the subspaces e ne for two arbitrary partitions and are also constructed and the dimensions of these spaces are given a combinatorial interpretation in terms of the so called decreasing factorization of an arbitary word into a product of lyndon words

reduction to real infinitesimal character in affine hecke algebras the main result of this paper is to show that the problem of the determination of the unramified unitary dual of a split p adic group is equivalent to the problem of determining the unitary dual of the corresponding graded hecke algebra in bm the authors established this equivalence in the case of iwahori spherical representations under a certain restriction namely it was essential for the infinitesimal character to be real in the terminology of bmj in terms of the langlands deligne lusztig parameters s u p kul the restriction is that s e lg be a purely hyperbolic element the technique used in bm was to combine the notion of the signature of a k character in v with some facts which follow from kl namely that the 2w characters of tempered representations are linearly independent this is essentially true precisely when the infinitesimal character is real for if not s has an elliptic part se such that

exact solutions of exactly integrable quantum chains by a matrix product ansatz most of the exact solutions of quantum one dimensional hamiltonians are obtained thanks to the success of the bethe ansatz on its several formulations according to this ansatz the amplitudes of the eigenfunctions of the hamiltonian are given by a sum of permutations of appropriate plane waves in this paper alternatively we present a matrix product ansatz that asserts that those amplitudes are given in terms of a matrix product the eigenvalue equation for the hamiltonian defines the algebraic properties of the matrices defining the amplitudes the consistency of the commutativity relations among the elements of the algebra implies the exact integrability of the model the matrix product ansatz we propose allows an unified and simple formulation of several exact integrable hamiltonians in order to introduce and illustrate this ansatz we present the exact solutions of several quantum chains with one and two global conservation laws and periodic boundaries such as the xxz chain spin 1 fateev zamolodchikov model izergin korepin model sutherland model t j model hubbard model etc formulation of the matrix product ansatz for quantum chains with open ends is also possible as an illustration we present the exact solution of an extended xxz chain with z magnetic fields at the surface and arbitrary hard core exclusion among the spins

r matrices of three state hamiltonians solvable by coordinate bethe ansatz we review some of the strategies that can be implemented to infer an r matrix from the knowledge of its hamiltonian we apply them to the classification achieved in crampe frappat and ragoucy j phys a 46 405001 2013 on three state u 1 invariant hamiltonians solvable by coordinate bethe ansatz focusing on models for which the s matrix is not trivial for the 19 vertex solutions we recover the r matrices of the well known zamolodchikov fateev and izergin korepin models we point out that the generalized bariev hamiltonian is related to both main and special branches studied by martins in nucl phys b 874 243 2013 that we prove to generate the same hamiltonian the 19 vertex spr model still resists to the analysis although we are able to state some no go theorems on its r matrix for 17 vertex hamiltonians we produce a new r matrix

partitional fuzzy clustering methods based on adaptive quadratic distances this paper presents partitional fuzzy clustering methods based on adaptive quadratic distances the methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances these distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another moreover various fuzzy partition and cluster interpretation tools are introduced experiments with real and synthetic data sets show the usefulness of these adaptive fuzzy clustering methods and the merit of the fuzzy partition and cluster interpretation tools

the mathbb a _ q t algebra and parabolic flag hilbert schemes the earlier work of the first and the third name authors introduced the algebra mathbb a q t and its polynomial representation in this paper we construct an action of this algebra on the equivariant k theory of certain smooth strata in the flag hilbert scheme of points on the plane in this presentation the fixed points of the torus action correspond to generalized macdonald polynomials and the matrix elements of the operators have an explicit presentation

representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the yang baxter equation quantum doubles of finite group algebras form a class of quasitriangular hopf algebras that algebraically solve the yang baxter equation each representation of the quantum double then gives a matrix solution of the yang baxter equation such solutions do not depend on a spectral parameter and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups dn these results may be used to determine constant solutions of the yang baxter equation we then discuss baxterization ansatze to obtain solutions of the yang baxter equation with a spectral parameter and give several examples including a new 21 vertex model we also describe this approach in terms of minimal dimensional representations of the quantum doubles of the alternating group a4 and the symmetric group s4

the yang baxter equation for mathcal pt invariant 19 vertex models we study the solutions of the yang baxter equation associated with 19 vertex models invariant by the parity time symmetry from the perspective of algebraic geometry we determine the form of the algebraic curves constraining the respective boltzmann weights and find that they possess a universal structure this allows us to classify the integrable manifolds into four different families reproducing three known models besides uncovering a novel 19 vertex model in a unified way the introduction of the spectral parameter on the weights is made via the parameterization of the fundamental algebraic curve which is a conic the diagonalization of the transfer matrix of the new vertex model and its thermodynamic limit properties are discussed we point out a connection between the form of the main curve and the nature of the excitations of the corresponding spin 1 chains

completely splittable representations of symmetric groups and affine hecke algebras abstract we study the class of completely splittable representations of the symmetric group and its associated degenerate affine hecke algebra in positive characteristic using techniques developed by okounkov and vershik for the symmetric group over the complex numbers the representations are classified and constructed and we provide a character formula in the symmetric group case

a construction of coxeter group representations ii abstract an axiomatic approach to the representation theory of coxeter groups and their hecke algebras was presented in r m adin f brenti y roichman a unified construction of coxeter group representations i adv appl math in press arxiv math rt 0309364 combinatorial aspects of this construction are studied in this paper in particular the symmetric group case is investigated in detail the resulting representations are completely classified and include the irreducible ones

semigroups of sl_3 mathbb c tensor product invariants abstract we find presentations for a family of semigroup algebras related to the problem of decomposing sl 3 c tensor products along the way we find new toric degenerations of the grassmannian variety gr 3 c n which are t invariant for t gl n c the diagonal torus

the ak generalization of the o 1 loop model on a cylinder affine hecke algebra q kz equation and the sum rule we study the ak generalized model of the o 1 loop model on a cylinder the affine hecke algebra associated with the model is characterized by a vanishing condition the cylindric relation we present two representations of the algebra the first one is the spin representation and the other is in the vector space of states of the ak generalized model a state of the model is a natural generalization of a link pattern we propose a new graphical way of dealing with the yang baxter equation and q symmetrizers by the use of the rhombus tiling the relation between two representations and the meaning of the cylindric relations are clarified through the rhombus tiling the sum rule for this model is obtained by solving the q kz equation at the razumov stroganov point

unitary representations of cyclotomic rational cherednik algebras abstract we classify the irreducible unitary modules in category o c for the rational cherednik algebras of type g r 1 n and give explicit combinatorial formulas for their graded characters more precisely we produce a combinatorial algorithm determining for each r partition of n the closed semi linear set of parameters c for which the contravariant form on the irreducible representation l c is positive definite we use this algorithm to give a closed form answer for the cherednik algebra of the symmetric group recovering a result of etingof stoica and the author and the weyl groups of classical type

a vanishing theorem for dirac cohomology of standard modules abstract this paper studies the dirac cohomology of standard modules in the setting of graded hecke algebras with geometric parameters we prove that the dirac cohomology of a standard module vanishes if and only if the module is not twisted elliptic tempered the proof makes use of two deep results one is some structural information from the generalized springer correspondence obtained by s kato and lusztig another one is a computation of the dirac cohomology of tempered modules by barbasch ciubotaru trapa and ciubotaru we apply our result to compute the dirac cohomology of ladder representations for type a n for each of such representations with non zero dirac cohomology we associate to a canonical weyl group representation we use the dirac cohomology to conclude that such representations appear with multiplicity one