towers of recollement and bases for diagram algebras planar diagrams and a little beyond abstract the recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor the method is hence adapted to treat sequences that are not necessarily towers by inclusion such as symplectic blob algebras diagram algebra quotients of the type c hecke algebras by carefully reviewing the diagram algebra construction we find a new set of functors interrelating module categories of ordinary blob algebras diagram algebra quotients of the type b hecke algebras at different values of the algebra parameters we show that these functors generalise to determine the structure of symplectic blob algebras and hence of certain two boundary temperley lieb algebras arising in statistical mechanics we identify the diagram basis with a cellular basis for each symplectic blob algebra and prove that these algebras are quasihereditary over a field for almost all parameter choices and generically semisimple that is we give bases for all cell and standard modules

on the blocks of the walled brauer algebra we determine the blocks of the walled brauer algebra in characteristic zero these can be described in terms of orbits of the action of a weyl group of type a on a certain set of weights in positive characteristic we give a linkage principle in terms of orbits of the corresponding affine weyl group we also classify the semisimple walled brauer algebras in all characteristics

decomposition numbers for the cyclotomic brauer algebras in characteristic zero we study the representation theory of the cyclotomic brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical brauer algebras in particular we determine the block structure and decomposition numbers in characteristic zero

perturbed proximal point algorithms for general quasi variational like inclusions in this paper we introduce two new concepts of subdifferential and proximal mappings of proper functionals on hilbert spaces the existence and lipschitz continuity of proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of general quasi variational like inclusions and develop some new perturbed proximal point algorithms of mann and ishikawa type for finding the approximate solutions of the general quasi variational like inclusions the convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed our algorithms and results improve and generalize many known results in the literature

cellular algebras and inverse semigroups abstract we show that under certain compatability assumptions the semigroup algebra of an inverse semigroup is cellular if the group algebras of its maximal subgroups are cellular motivating examples include the symmetric inverse semigroup also known as the rook monoid and the dual symmetric inverse semigroup

projection methods algorithms and a new system of nonlinear variational inequalities abstract the convergence of projection methods is based on a new iterative algorithm for the approximation solvability of the following system of nonlinear variational inequalities snvi determine elements x y k such that t y x y x x 0 for all x k and for 0 and t x y x x y 0 for all x k and for 0 where t k h is a mapping from a nonempty closed convex subset k of a real hilbert space h into h this new class of generalized nonlinear variational inequalities reduces to standard class of nonlinear variational inequalities which are widely studied and applied to various problems arising from mathematical sciences optimization and control theory and other related fields

recollements of self injective algebras and classification of self injective diagram algebras diagram algebras in particular brauer algebras birman murakami wenzl algebras and partition algebras are used in representation theory and invariant theory of orthogonal and symplectic groups in knot theory in mathematical physics and elsewhere classifications are known when such algebras are semisimple of finite global dimension or quasi hereditary we obtain a characterisation of the self injective case which is shown to coincide with the previously also unknown symmetric case the main tool is to show that indecomposable self injective algebras in general are derived simple that is their bounded derived module categories admit trivial recollements only as a consequence self injective algebras are seen to satisfy a derived jordan holder theorem

nonlinear relaxed cocoercive variational inclusions involving a η accretive mappings in banach spaces in this paper we introduce a new concept of a h accretive mappings which generalizes the existing monotone or accretive operators we study some properties of a h accretive mappings and define resolvent operators associated with a h accretive mappings by using the new resolvent operator technique we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed cocoercive variational inclusions involving a h accretive mappings and study applications of a h accretive mappings to the approximation solvability of this class of nonlinear relaxed cocoercive variational inclusions in q uniformly smooth banach spaces our results improve and generalize the corresponding results of recent works

cohomological stratification of diagram algebras the class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras while the definition is in combinatorial terms by adding extra structure to graham and lehrer s definition of cellular algebras various structural properties are established in terms of exact functors and stratifications of derived categories the stratifications relate large algebras such as brauer algebras to smaller ones such as group algebras of symmetric groups among the applications are relative equivalences of categories extending those found by hemmer and nakano and by hartmann and paget as well as identities between decomposition numbers and cohomology groups of large and small algebras

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

a perturbed algorithm for variational inclusions a perturbed method for solving a new class of variational inclusions is presented and a convergence result which includes as a special case some known results in this field is given

mann and ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions abstract in this paper we introduce a class of generalized quasivariational inclusions and show its equivalence with a class of fixed point problems by making use of the properties of proximal maps using this equivalence we develop the mann and ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions further using fixed point techniques we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms our algorithms and results improve and generalize many known corresponding algorithms and results

spectral theory of pauli fierz operators abstract we study spectral properties of pauli fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field we give precise estimates of the location and multiplicity of the singular spectrum of such operators applications of these estimates which will be discussed elsewhere concern spectral and ergodic theory of non relativistic qed our proof has two ingredients the feshbach method which is developed in an abstract framework and mourre theory applied to the operator restricted to the sector orthogonal to the vacuum

a family of modules with specht and dual specht filtrations abstract we study the permutation module arising from the action of the symmetric group s 2 n on the conjugacy class of fixed point free involutions defined over an arbitrary field the indecomposable direct summands of these modules are shown to possess filtrations by specht modules and also filtrations by dual specht modules we see that these provide counterexamples to a conjecture by hemmer twisted permutation modules are also considered as is an application to the brauer algebra

a new system of variational inclusions with h η monotone operators in hilbert spaces in this paper we introduce and study a new system of variational inclusions involving h h monotone operators in hilbert space using the resolvent operator associated with h h monotone operators we prove the existence and uniqueness of solutions for this new system of variational inclusions we also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm

young modules and filtration multiplicities for brauer algebras we define permutation modules and young modules for the brauer algebra bk r and show that if the characteristic of the field k is neither 2 nor 3 then every permutation module is a sum of young modules respecting an ordering condition similar to that for symmetric groups moreover we determine precisely in which cases cell module filtration multiplicities are well defined as done by hemmer and nakano for symmetric groups

ground states and spectrum of quantum electrodynamics of nonrelativistic particles a system consisting of finitely many nonrelativistic particles bound on an external potential and minimally coupled to a massless quantized radiation field without the dipole approximation is considered an ultraviolet cut off is imposed on the quantized radiation field the hamiltonian of the system is defined as a self adjoint operator in a hilbert space the existence of the ground states of the hamiltonian is established it is shown that there exist asymptotic annihilation and creation operators hence the location of the absolutely continuous spectrum of the hamiltonian is specified

on the semisimplicity of the cyclotomic brauer algebras ii abstract in this paper we give a necessary and sufficient condition for the semisimplicity of cyclotomic brauer algebras b m n of types g m 1 n with m 2 this generalizes h rui a criterion on the semisimple brauer algebras j combin theory ser a 111 2005 78 88 1 2 1 3 and h rui m si a criterion on the semisimple brauer algebras ii j combin theory ser a 113 2006 1199 1203 2 5 on brauer algebras

decomposition numbers of quantized walled brauer algebras in this paper we establish an explicit relationship between decomposition numbers of quantized walled brauer algebras and those for either hecke algebras associated to certain symmetric groups or rational q schur algebras over a field kappa this enables us to use ariki s result j math kyoto univ 36 4 789 808 1996 and varagnolo vasserot s result duke math j 100 2 267 297 1999 to compute such decomposition numbers via inverse kazhdan lusztig polynomials associated with extended affine weyl groups of type a if the ground field is mathbb c

strong symmetry defined by twisting modules applied to quasi hereditary algebras with triangular decomposition and vanishing radical cube for a finite dimensional algebra with triangular decomposition a new kind of modules is defined the twisting modules using the structure of these modules for some algebras with vanishing radical cube the characteristic tilting module is described and its endomorphism ring is computed this covers both temperley lieb algebras and q schur algebras of finite representation type our basic tool is a new symmetry condition stronger than the symmetry provided by the existence of a triangular decomposition in general

affine cellular algebras abstract graham and lehrer have defined cellular algebras and developed a theory that allows in particular to classify simple representations of finite dimensional cellular algebras many classes of finite dimensional algebras including various hecke algebras and diagram algebras have been shown to be cellular and the theory due to graham and lehrer successfully has been applied to these algebras we will extend the framework of cellular algebras to algebras that need not be finite dimensional over a field affine hecke algebras of type a and infinite dimensional diagram algebras like the affine temperley lieb algebras are shown to be examples of our definition the isomorphism classes of simple representations of affine cellular algebras are shown to be parameterised by the complement of finitely many subvarieties in a finite disjoint union of affine varieties in this way representation theory of non commutative algebras is linked with commutative algebra moreover conditions on the cell chain are identified that force the algebra to have finite global cohomological dimension and its derived category to admit a stratification these conditions are shown to be satisfied for the affine hecke algebra of type a if the quantum parameter is not a root of the poincare polynomial

a specht filtration of an induced specht module abstract let h n be a degenerate or non degenerate hecke algebra of type g l 1 n defined over a commutative ring r with one and let s be a specht module for h n this paper shows that the induced specht module s h n h n 1 has an explicit specht filtration

diagrammatic kazhdan lusztig theory for the walled brauer algebra we determine the decomposition numbers for the brauer and walled brauer algebras in characteristic zero in terms of certain polynomials associated to cap and curl diagrams recovering a result of martin in the brauer case we consider a second family of polynomials associated to such diagrams and use these to determine projective resolutions of the standard modules we then relate these two families of polynomials to kazhdan lusztig theory via the work of lascoux schutzenberger and boe inspired by work of brundan and stroppel in the cap diagram case

on the existence and uniqueness of ground states of a generalized spin boson model a generalization of the standard spin boson model is considered the hamiltonianh of the model with a coupling parameter racts in the tensor product h fbof a hilbert space h and the boson symmetric fock space fboverl2 r the existence and uniqueness of ground states ofh are investigated the degeneracy of the ground states is also discussed the results obtained arenonperturbative the methods used are those of constructive quantum field theory and the min max principle an exact asymptotic formula for the ground state energy ofh as is also established

iterative algorithm for a system of nonlinear variational like inclusions in this paper we consider a system of nonlinear variational like inclusions snvli in hilbert spaces in particular snvli reduces to a variational inclusion an extension of variational inclusion studied by h a s s o u n i a n d m o u d a f i 1 using fixed point method we suggest an iterative algorithm for finding an approximate solution to snvli further we prove the existence of solution and discuss convergence criteria for the approximate solution of snvli the theorems presented in this paper improve and unify many known results of variational inclusions and variational inequalities see for example 1 3

iterative methods for solving variational inclusions in banach spaces in this paper we consider a system of nonlinear variational inclusions involving h accretive operators studied by huang and fang in q uniformly smooth banach spaces using resolvent operator technique we suggest an iterative algorithm for finding an approximate solution to the system of variational inclusions further we discuss convergence criteria for the approximate solution of the system of variational inclusions the theorems presented in this paper improve and unify many known results of variational inclusions

iterative algorithms for a new system of nonlinear variational inclusions with a η accretive mappings in banach spaces in this paper we introduce and study a new system of nonlinear variational inclusions with a h accretive mappings in banach spaces by using the resolvent operator associated with a h accretive mappings we construct some new iterative algorithms for approximating the solution of this system of variational inclusions we also prove the existence of solutions and the convergence of the sequences generated by the algorithm in banach spaces the results presented in this paper extend and improve some known results in the literature

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

morita equivalence for cyclotomic bmw algebras abstract in this paper we determine explicitly the singular parameters for cyclotomic bmw algebras b r n over an arbitrary field equivalently we give a criterion for b r n being morita equivalent to the direct sum of some ariki koike algebras this generalizes konig and xi s work on brauer algebras 14 theorem 7 3 and our previous work on brauer and birman murakami wenzl algebras 20 proposition 2 15

a tower construction for the radical in brauer s centralizer algebras abstract in this paper we study the structure of the brauer centralizer algebras in the case that the multiplication constant x is a rational integer several authors have studied the structure of these algebras for generic values of x in particular hans wenzl showed that the brauer algebras can be obtained from jones basic construction and he used that fact to prove that the brauer algebras are semisimple when x is not a rational integer the tower construction is a method to study towers of semisimple algebras hence it does not apply in our case where the algebras in the tower eventually have radicals our first step in this paper is to modify the tower construction so that it does a simultaneous tower construction of the radicals and the semisimple quotients of a tower of algebras the rest of the paper is devoted to describing these constructions explicitly in the brauer algebra case one surprising corollary of this method is a connection between two seemingly distinct criteria for the simplicity of certain subrings of the brauer algebras it is possible to identify explicitly certain subrings of the brauer algebras which are the matrix rings corresponding to irreducible representations in the semisimple case in previous work these authors gave a combinatorial condition for simplicity of these individual matrix rings when x is a rational integer the tower construction gives a second algebraic condition for simplicity it is difficult to see why these two conditions are equivalent however the methods used in this paper make that clear

perturbed algorithms and sensitivity analysis for a general class of variational inclusions in the present paper we study a perturbed iterative method for solving a general class of variational inclusions an existence result which generalizes some known results in this field a convergence result and a new iterative method are given we also prove the continuity of the perturbed solution to a parametric variational inclusion problem several special cases are discussed

spectral theory of massless pauli fierz models we study the spectral theory of massless pauli fierz models using an extension of the mourre method we prove the local finiteness of point spectrum and a limiting absorption principle away from the eigenvalues for an arbitrary coupling constant in addition we show that the expectation value of the number operator is finite on all eigenvectors

iterated inflations of cellular algebras abstract we present a result characterising iterated inflations of cellular algebras derived from the work of konig and xi this result is intended to replace an incorrect proposition in the literature and gives explicit and readily checked conditions which establish that an algebra is an iterated inflation of cellular algebras and hence is cellular with cellular data directly related to the cellular data of the constituent cellular algebras

schur algebras of brauer algebras i a classical problem of invariant theory and of lie theory is to determine endomorphism rings of representations of classical groups for instance of tensor powers of the natural module schur weyl duality or of full direct sums of tensor products of exterior powers ringel duality in this article the endomorphism rings of full direct sums of tensor products of symmetric powers over symplectic and orthogonal groups are determined these are shown to be isomorphic to schur algebras of brauer algebras as defined in henke and koenig math z 272 3 4 729 759 2012 this implies structural properties of the endomorphism rings such as double centraliser properties quasi hereditary and a universal property as well as a classification of simple modules

on the radical of brauer algebras the radical of the brauer algebra mathcal b f x is known to be non trivial when the parameter x is an integer subject to certain conditions with respect to f in these cases we display a wide family of elements in the radical which are explicitly described by means of the diagrams of the usual basis of mathcal b f x the proof is by direct approach for x 0 and via classical invariant theory in the other cases exploiting then the well known representation of brauer algebras as centralizer algebras of orthogonal or symplectic groups acting on tensor powers of their standard representation this also gives a great part of the radical of the generic indecomposable mathcal b f x modules we conjecture that this part is indeed the whole radical in the case of modules and it is the whole part in a suitable step of the standard filtration in the case of the algebra as an application we find some more precise results for the module of pointed chord diagrams and for the temperley lieb algebra realised inside mathcal b f 1 acting on it ahi quanto a dir che sia e cosa dura lo radical dell algebra di brauer pur se l pensier gia muove a congettura n barbecue scholia

a characteristic free approach to brauer algebras brauer algebras arise in representation theory of orthogonal or symplectic groups these algebras are shown to be iterated inflations of group algebras of symmetric groups in particular they are cellular as had been shown before by graham and lehrer this gives some information about block decomposition of brauer algebras

mann and ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi variational inclusions abstract in this paper we introduce a new class of generalized nonlinear implicit quasi variational inclusions and prove its equivalence with a class of fixed point problems by making use of the properties of maximal monotone we also prove the existence of solutions for this generalized nonlinear implicit quasi variational inclusions and the convergence of iterative sequences generated by the perturbed algorithms

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

h monotone operator and resolvent operator technique for variational inclusions in this paper we introduce a new class of monotone operators h monotone operators the resolvent operator associated with an h monotone operator is defined and its lipschitz continuity is presented we also introduce and study a new class of variational inclusions involving h monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures

the brauer algebra and the symplectic schur algebra let k be an algebraically closed field of characteristic p 0 let m r be integers with m 1 r 0 and m r and let s0 2m r be the symplectic schur algebra over k as introduced by the first author we introduce the symplectic schur functor derive some basic properties of it and relate this to work of hartmann and paget we do the same for the orthogonal schur algebra we give a modified jantzen sum formula and a block result for the symplectic schur algebra under the assumption that r and the residue of 2m mod p are small relative to p from this we deduce a block result for the orthogonal schur algebra under similar assumptions we also show that in general the block relations of the brauer algebra and the symplectic and orthogonal schur algebra are the same finally we deduce from the previous results a new proof of the description of the blocks of the brauer algebra in characteristic 0 as obtained by cox de visscher and martin

ground states of the massless derezinski gerard model we consider the massless derezinski gerard model introduced by derezinski and gerard in 1999 we give a sufficient condition for the existence of a ground state of the massless derezinski gerard model without the assumption that the hamiltonian of particles has compact resolvent