representation type for block algebras of hecke algebras of classical type abstract we find representation type of the cyclotomic quiver hecke algebras r of level two in affine type a in particular we have determined representation type for all the block algebras of hecke algebras of classical type except for characteristic two in type d which has not been known for a long time as an application of this result we prove that block algebras of finite representation type are brauer tree algebras whose brauer trees are straight lines without exceptional vertex if the hecke algebras are of classical type in good characteristic we conjecture that this statement should hold for hecke algebras of exceptional type

indefinite quadratic with linear costs optimal control of markov jump with multiplicative noise systems in this paper we consider the stochastic optimal control problem of discrete time markov jump with multiplicative noise linear systems the performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables the weighting matrices of the state and control for the quadratic part are allowed to be indefinite we present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized riccati difference equations interconnected with a set of coupled linear recursive equations for the case in which the quadratic term matrices are non negative this necessary and sufficient condition can be written in a more explicit way the results are applied to a problem of portfolio optimization

on a theorem of benson and curtis iwahori conjectured 5 that the hecke algebra over q of a chevalley group g over a finite field f with respect to a bore1 subgroup is isomorphic to the group algebra over q of the weyl group the analogous statement with q replaced by its algebraic closure was proved by tits 3 ex 27 p 561 using a deformation argument in 11 benson and curtis proved using a case by case analysis that iwahori s conjecture is true over q whenever g is simple of type ze e with the help of springer they proved that when g is of type e or e there exists irreducible representations of the hecke algebra whose character involve 4 and hence iwahori s conjecture over q is false in general the main result of this paper is an explicit construction of an isomorphism of the hecke algebra over q q with the group algebra over q q of the weyl group the construction makes essential use of the polynomials p w of 8 at some point in the proof i have to appeal to the interpretation of p l in terms of multiplicities in verma modules 8 i 51 which has recently been established by brylinski and kashiwara 4 and independently by belinson and bernstein

stochastic linear quadratic control with conic control constraints on an infinite time horizon this paper is concerned with a stochastic linear quadratic lq control problem in the infinite time horizon where the control is constrained in a given arbitrary closed cone the cost weighting matrices are allowed to be indefinite and the state is scalar valued first the mean square conic stabilizability of the system is defined which is then characterized by a set of simple conditions involving linear matrix inequalities lmis next the issue of well posedness of the underlying optimal lq control which is necessitated by the indefiniteness of the problem is addressed in great detail and necessary and sufficient conditions of the well posedness are presented on the other hand to address the lq optimality two new algebraic equations a la riccati called extended algebraic riccati equations eares along with the notion of their stabilizing solutions are introduced for the first time optimal feedback control as well as the optimal value are explicitly derived in terms of the stabilizing solutions to the eares moreover several cases when the stabilizing solutions do exist are discussed and algorithms of computing the solutions are presented finally numerical examples are provided to illustrate the theoretical results established

multiple rademacher means and their applications abstract we evaluate multiple rademacher means for various classes of multilinear operators under the assumption that the range has cotype q these results show that the class of multiple q 2 summing operators plays an important role further we get new extensions of bu s theorem in the multilinear case

on the cohen strongly p summing multilinear operators abstract in this paper we introduce and study a new concept of summability in the category of multilinear operators which is the cohen strongly p summing multilinear operators we prove a natural analog of the pietsch domination theorem and we compare the notion of p dominated multilinear operators with this class by generalizing a theorem of bu cohen

hecke algebras of finite type are cellular let mathcal h be the one parameter hecke algebra associated to a finite weyl group w defined over a ground ring in which bad primes for w are invertible using deep properties of the kazhdan lusztig basis of mathcal h and lusztig s a function we show that mathcal h has a natural cellular structure in the sense of graham and lehrer thus we obtain a general theory of specht modules for hecke algebras of finite type previously a general cellular structure was only known to exist in types an and bn

the combinatorics of twisted involutions in coxeter groups the open intervals in the bruhat order on twisted involutions in a coxeter group are shown to be pl spheres this implies results conjectured by f incitti and sharpens the known fact that these posets are gorenstein over z 2 we also introduce a boolean cell complex which is an analogue for twisted involutions of the coxeter complex several classical coxeter complex properties are shared by our complex when the group is finite it is a shellable sphere shelling orders being given by the linear extensions of the weak order on twisted involutions furthermore the h polynomial of the complex coincides with the polynomial counting twisted involutions by descents in particular this gives a type independent proof that the latter is symmetric

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

strongly p summing multilinear operators abstract we define the concept of strongly p summing multilinear operators and prove that they have properly defined aron berner extensions some properties and examples are shown

positivity conjectures for kazhdan lusztig theory on twisted involutions the finite case abstract let w s be any coxeter system and let w w be an involution of w which preserves the set of simple generators s lusztig and vogan have shown that the corresponding set of twisted involutions i e elements w w with w 1 w naturally generates a module of the hecke algebra of w s with two distinguished bases the transition matrix between these bases defines a family of polynomials p y w which one can view as a twisted analogue of the much studied family of kazhdan lusztig polynomials of w s the polynomials p y w can have negative coefficients but display several conjectural positivity properties of interest which parallel positivity properties of the kazhdan lusztig polynomials this paper reports on some calculations which verify four such positivity conjectures in several finite cases of interest in particular for the non crystallographic coxeter systems of types h 3 and h 4

some techniques on nonlinear analysis and applications in this paper we present two different results in the context of nonlinear analysis the first one is essentially a nonlinear technique that in view of its strong generality may be useful in different practical problems the second result more technical but also connected to the first one is an extension of the well known pietsch domination theorem the last decade witnessed the birth of different families of pietsch domination type results and some attempts of unification our result that we call full general pietsch domination theorem is potentially a definitive pietsch domination theorem which unifies the previous versions and delimits what can be proved in this line the connections to the recent notion of weighted summability are traced

james conjecture for hecke algebras of exceptional type i in this paper and a second part to follow we complete the programme initiated more than 15 years ago of determining the decomposition numbers and verifying james conjecture for iwahori hecke algebras of exceptional type the new ingredients which allow us to achieve this aim are the fact recently proved by the rst author that all hecke algebras of nite type are cellular in the sense of graham lehrer and the explicit determination of w graphs for the irreducible generic representations of hecke algebras of type e7 and e8 by howlett and yin thus we can reduce the problem of computing decomposition numbers to a manageable size where standard techniques e g parker s meataxe and its variations can be applied in this part we describe the theoretical foundations for this procedure

well posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon abstract this paper is concerned with a stochastic linear quadratic lq problem in an infinite time horizon with multiplicative noises both in the state and the control a distinctive feature of the problem under consideration is that the cost weighting matrices for the state and the control are allowed to be indefinite a new type of algebraic riccati equation called a generalized algebraic riccati equation gare is introduced which involves a matrix pseudo inverse and two additional algebraic equality inequality constraints it is then shown that the well posedness of the indefinite lq problem is equivalent to a linear matrix inequality lmi condition whereas the attainability of the lq problem is equivalent to the existence of a stabilizing solution to the gare moreover all possible optimal controls are identified via the solution to the gare finally it is proved that the solution to the gare can be obtained via solving a convex optimization problem called semidefinite programming

two lipschitz operator ideals abstract we introduce and investigate the concept of two lipschitz operator ideal between pointed metric spaces and banach spaces we show the basics of this new theory and we give a procedure to create a two lipschitz operator ideal from a linear operator ideal we apply our result to the ideals of strongly p summing and compact linear operator to obtain their corresponding two lipschitz operator ideal also we establish a natural relation between two lipschitz and bilinear maps and show that the two lipschitz factorable p dominated operators are those which are associated to the well known p semi integral bilinear operators

cellularity of the lowest two sided ideal of an affine hecke algebra abstract in this paper we show that the lowest two sided ideal of an affine hecke algebra is affine cellular for all choices of parameters we explicitly describe the cellular basis and we show that the basis elements have a nice decomposition when expressed in the kazhdan lusztig basis in type a we provide a combinatorial description of this decomposition in term of number of paths

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

characterizing all optimal controls for an indefinite stochastic linear quadratic control problem this paper is concerned with a stochastic linear quadratic lq control problem in the infinite time horizon with indefinite state and control weighting matrices in the cost function it is shown that the solvability of this problem is equivalent to the existence of a so called static stabilizing solution to a generalized algebraic riccati equation moreover another algebraic riccati equation is introduced and all the possible optimal controls including the ones in state feedback form of the underlying lq problem are explicitly obtained in terms of the two riccati equations

technical communique an equivalence result in linear quadratic theory we consider the zero endpoint infinite horizon lq problem we show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic riccati equation this result is shown without assuming positive definiteness of the state weighting matrix the feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback nash equilibria both in a deterministic and stochastic context

an abstract result on cohen strongly summing operators abstract we present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of cohen strongly summing linear operators our argument is extended to multilinear operators and as a consequence we establish some alternative characterizations for the class of cohen strongly summing multilinear operators

stabilization control for ito stochastic system with indefinite state and control weight costs in standard linear quadratic lq control the first step in investigating infinite horizon optimal control is to derive the stabilisation condition with the optimal lq controller this paper focus

cellular structures on hecke algebras of type b abstract the aim of this paper is to gather and try to unify several approaches for the modular representation theory of hecke algebras of type b we attempt to explain the connections between geck s cellular structures coming from kazhdan lusztig theory with unequal parameters and ariki s theorem on the canonical basis of the fock spaces

quiver mutations and boolean reflection monoids abstract in 2010 everitt and fountain introduced the concept of reflection monoids the boolean reflection monoids form a family of reflection monoids symmetric inverse semigroups are boolean reflection monoids of type a in this paper we give a family of presentations of boolean reflection monoids and show how these presentations are compatible with quiver mutations of orientations of dynkin diagrams with frozen vertices our results recover the presentations of boolean reflection monoids given by everitt and fountain and the presentations of symmetric inverse semigroups given by popova respectively surprisingly inner by diagram automorphisms of irreducible weyl groups and boolean reflection monoids can be constructed by sequences of mutations preserving the same underlying diagrams besides we show that semigroup algebras of boolean reflection monoids are cellular algebras

on summability of nonlinear mappings a new approach the main goal of this paper is to characterize arbitrary nonlinear non multilinear mappings f x 1 times cdots times x n rightarrow y between banach spaces that satisfy a quite natural pietsch domination type theorem around a given point a 1 ldots a n in x 1 times cdots times x n as a consequence of our approach a notion of weighted summability arises naturally which may be an interesting topic for further investigation

discrete time mean variance optimal control of linear systems with markovian jumps and multiplicative noise in this article we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output in the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system we present explicit sufficient conditions for the existence of an optimal control strategy for these problems generalising previous results in the literature we conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching

affine cellularity of affine hecke algebras of rank two we show that affine hecke algebras of rank two with generic parameters are affine cellular in the sense of koenig xi

relationship between backward stochastic differential equations and stochastic controls a linear quadratic approach it is well known that backward stochastic differential equations bsdes stem from the study on the pontryagin type maximum principle for optimal stochastic controls a solution of a bsde hits a given terminal value which is a random variable by virtue of an it additional martingale term and an indefinite initial state this paper attempts to explore the relationship between bsdes and stochastic controls by interpreting bsdes as some stochastic optimal control problems more specifically associated with a bsde a new stochastic control problem is introduced with the same dynamics but a definite given initial state the martingale term in the original bsde is regarded as the control and the objective is to minimize the second moment of the difference between the terminal state and the terminal value given in the bsde this problem is solved in a closed form by the stochastic linear quadratic lq theory developed recently the general result is then applied to the black scholes model where an optimal mean variance hedging portfolio is obtained explicitly in terms of the option price finally a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account

discrete time lqg controls with control dependent noise this paper presents some studies on partially observed linear quadratic gaussian lqg models where the stochastic disturbances depend on both the states and the controls and the measurements are bilinear in the noise and the states controls while the separation theorem of standard lqg design does not apply suboptimal linear state estimate feedback controllers are derived based on certain linearizations the controllers are useful for nonlinear stochastic systems where the linearized models include terms bilinear in the noise and states controls and are significantly more accurate than if the bilinear terms are set to zero the controllers are calculated by solving a generalized discrete time riccati equation which in turn has properties relating to well posedness of the associated lqg problem

absolutely continuous multilinear operators abstract we introduce the new class of the p p 1 p m absolutely continuous multilinear operators that is defined using a summability property that provides the multilinear version of the p absolutely continuous operators we give an analogue of the pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for p absolutely continuous operators obtaining in this way a rich factorization theory we present also a tensor norm which represents this multi ideal by trace duality as an application we show that p p 1 p m absolutely continuous multilinear operators are compact under some requirements applications to factorization of linear maps on banach function spaces through interpolation spaces are also given

quadratic and h switching control for discrete time linear systems with multiplicative noises the goal of this paper is to study the switched stochastic control problem of discrete time linear systems with multiplicative noises we consider both the quadratic and the h criteria for the performance evaluation initially we present a sufficient condition based on some lyapunov metzler inequalities to guarantee the stochastic stability of the switching system moreover we derive a sufficient condition for obtaining a metzler matrix that will satisfy the lyapunov metzler inequalities by directly solving a set of linear matrix inequalities and not bilinear matrix inequalities as usual in the literature of switched systems we believe that this result is an interesting contribution on its own in the sequel we present sufficient conditions again based on lyapunov metzler inequalities to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and h performance costs are bounded above by a constant value these results are illu

optimal mean variance control for discrete time linear systems with markovian jumps and multiplicative noises in this paper we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noises under two criteria the first one is an unconstrained mean variance trade off performance criterion along the time and the second one is a minimum variance criterion along the time with constraints on the expected output we present explicit conditions for the existence of an optimal control strategy for the problems generalizing previous results in the literature we conclude the paper by presenting a numerical example of a multi period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor

motzkin monoids and partial brauer monoids we study the partial brauer monoid and its planar submonoid the motzkin monoid we conduct a thorough investigation of the structure of both monoids providing information on normal forms green s relations regularity ideals idempotent generation minimal idempotent generating sets and so on we obtain necessary and sufficient conditions under which the ideals of these monoids are idempotent generated we find formulae for the rank smallest size of a generating set of each ideal and for the idempotent rank smallest size of an idempotent generating set of the idempotent generated subsemigroup of each ideal in particular when an ideal is idempotent generated the rank and idempotent rank are equal along the way we obtain a number of results of independent interest and we demonstrate the utility of the semigroup theoretic approach by applying our results to obtain new proofs of some important representation theoretic results concerning the corresponding diagram algebras the partial or rook brauer algebra and motzkin algebra

stochastic frequency characteristics this paper is concerned with stochastic linear quadratic lq problems in infinite time horizon with control dependent diffusions and indefinite cost weighting matrices the classical approach of frequency domain is employed to tackle the problem starting with the introduction of a frequency characteristic the equivalence is established among the unique solvability of the lq problem the solvability of the associated stochastic riccati equation the coercivity of some bilinear form in the hilbert space of the admissible controls and the uniformly positive definiteness of the frequency characteristic matrix

fixed points of involutive automorphisms of the bruhat order abstract applying a classical theorem of smith we show that the poset property of being gorenstein over z 2 is inherited by the subposet of fixed points under an involutive poset automorphism as an application we prove that every interval in the bruhat order on twisted involutions in an arbitrary coxeter group has this property and we find the rank function this implies results conjectured by f incitti we also show that the bruhat order on the fixed points of an involutive automorphism induced by a coxeter graph automorphism is isomorphic to the bruhat order on the fixed subgroup viewed as a coxeter group in its own right

hurwicz model of uncertain linear quadratic optimal control with jump abstractbased on hurwicz model of uncertain optimal control model with jump in this paper a hurwicz model of uncertain linear quadratic optimal control with jump is proposed then the necessary

multilinear variants of maurey and pietsch theorems and applications we prove composition results for multilinear operators and multilinear variants of maurey and pietsch theorems both for multiple p summing p dominated and p summing multilinear operators

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

canonical basic sets in type bn more than 10 years ago dipper james and murphy developed the theory of specht modules for hecke algebras of type bn more recently using lusztig s a function geck and rouquier showed how to obtain parametrizations of the irreducible representations of hecke algebras of any finite type in terms of so called canonical basic sets for certain values of the parameters in type bn combinatorial descriptions of these basic sets were found by jacon based on work of ariki and foda leclerc okado thibon welsh here we consider the canonical basic sets for all the remaining choices of the parameters

fully commutative elements in the weyl and affine weyl groups abstract let w be a weyl or an affine weyl group and let w c be the set of fully commutative elements in w we associate each w w c to a digraph g w by using g w we give a graph theoretic description for lusztig s a function on w c and describe explicitly all the distinguished involutions of w c the results verify two conjectures in our case one was proposed by myself in adv sci china math 3 1990 79 98 conjecture 8 10 and the other by lusztig in t asai et al open problems in algebraic groups in r hotta ed problems from the conference on algebraic groups and representations katata august 29 september 3 1983

positivity results for the hecke algebras of noncrystallographic finite coxeter groups abstract this paper is a report on a computer check of some important positivity properties of the hecke algebra in type h 4 including the nonnegativity of the structure constants in the kazhdan lusztig basis this answers a long standing question of lusztig s the same algorithm carried out by hand also allows us to deal with the case of dihedral coxeter groups

stochastic linear quadratic regulators with indefinite control weight costs this paper considers optimal minimizing control of stochastic linear quadratic regulators lqrs the assumption that the control weight costs must be positive definite inherited from the determ

on cohen almost summing multilinear operators abstract we show that all cohen strongly p summing multilinear operators and polynomials on banach spaces are cohen almost summing if the range space is a hilbert space then all cohen strongly p summing multilinear operators and polynomials are strongly q summing 1 p q moreover if both domain and range spaces are hilbert spaces then all hilbert schmidt multilinear operators are cohen strongly 2 summing

kazhdan lusztig cells and the murphy basis let h be the iwahori hecke algebra associated with s n the symmetric group on n symbols this algebra has two important bases the kazhdan lusztig basis and the murphy basis we establish a precise connection between the two bases allowing us to give for the first time purely algebraic proofs for a number of fundamental properties of the kazhdan lusztig basis and lusztig s results on the a function

computing kazhdan lusztig cells for unequal parameters abstract following lusztig we consider a coxeter group w together with a weight function l this gives rise to the pre order relation l and the corresponding partition of w into left cells we introduce an equivalence relation on weight functions such that in particular l is constant on equivalent classes we shall work this out explicitly for w of type f 4 and check that several of lusztig s conjectures concerning left cells with unequal parameters hold in this case even for those parameters which do not admit a geometric interpretation the proofs involve some explicit computations using chevie

how to compute the frobenius schur indicator of a unipotent character of a finite coxeter system abstract for each finite irreducible coxeter system w s lusztig has associated a set of unipotent characters uch w there is also a notion of a fourier transform on the space of functions uch w r due to lusztig for weyl groups and to broue lusztig and malle in the remaining cases this paper concerns a certain w representation w in the vector space generated by the involutions of w our main result is to show that the irreducible multiplicities of w are given by the fourier transform of a unique function uch w 1 0 1 which for various reasons serves naturally as a heuristic definition of the frobenius schur indicator on uch w the formula we obtain for extends prior work of casselman kottwitz lusztig and vogan addressing the case in which w is a weyl group we include in addition a succinct description of the irreducible decomposition of w derived by kottwitz when w s is classical and prove that w defines a gelfand model if and only if w s has type a n h 3 or i 2 m with m odd we show finally that a conjecture of kottwitz connecting the decomposition of w to the left cells of w holds in all non crystallographic types and observe that a weaker form of kottwitz s conjecture holds in general in giving these results we carefully survey the construction and notable properties of the set uch w and its attached fourier transform

stochastic optimal lqr control with integral quadratic constraints and indefinite control weights a standard assumption in traditional deterministic and stochastic optimal minimizing linear quadratic regulator lqr theory is that the control weighting matrix in the cost functional is strictly positive definite in the deterministic case this assumption is in fact necessary for the problem to be well posed because positive definiteness is required to make it a convex optimization problem however it has recently been shown that in the stochastic case when the diffusion term is dependent on the control the control weighting matrix may have negative eigenvalues but the problem remains well posed in this paper the completely observed stochastic lqr problem with integral quadratic constraints is studied sufficient conditions for the well posedness of this problem are given indeed we show that in certain cases these conditions may be satisfied even when the control weighting matrices in the cost and all of the constraint functionals have negative eigenvalues it is revealed that the seemingly nonconvex problem with indefinite control weights can actually be a convex one by virtue of the uncertainty in the system finally when these conditions are satisfied the optimal control is explicitly derived using results from duality theory