extensions of modules for twisted current algebras abstract twisted current algebras are fixed point subalgebras of current algebras under a finite group action special cases include equivariant map algebras and twisted forms of current algebras their finite dimensional simple modules fall into two categories those which factor through an evaluation map and those which do not we show that there are no nontrivial extensions between finite dimensional simple evaluation and non evaluation modules we then compute extensions between any pair of finite dimensional simple modules for twisted current algebras and use this information to study the block decomposition for the category in the special case of twisted forms this decomposition can be described in terms of maps to the fundamental group of the underlying root system

universal central extensions of twisted forms of split simple lie algebras over rings abstract we give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple lie algebra over a ring in particular the universal central extensions of twisted multiloop lie tori are obtained by the descent construction

quantum symmetric kac moody pairs the present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable kac moody algebras the resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras they give rise to triangular decompositions including a quantum analog of the iwasawa decomposition and they can be written explicitly in terms of generators and relations moreover their centers and their specializations are determined the constructions follow g letzter s theory of quantum symmetric pairs for semisimple lie algebras the main additional ingredient is the classification of involutive automorphisms of the second kind of symmetrizable kac moody algebras due to kac and wang the resulting theory comprises various classes of examples which have previously appeared in the literature such as q onsager algebras and the twisted q yangians introduced by molev ragoucy and sorba

branching in branch and price a generic scheme developing a branching scheme that is compatible with the column generation procedure can be challenging application specific and generic schemes have been proposed in the literature but they have their drawbacks one generic scheme is to implement standard branching in the space of the compact formulation to which the dantzig wolfe reformulation was applied however in the presence of multiple identical subsystems the mapping to the original variable space typically induces symmetries an alternative in an application specific context can be to expand the compact formulation to offer a wider choice of branching variables other existing generic schemes for use in branch and price imply modifications to the pricing problem this is a concern because the pricing oracle on which the method relies might become obsolete beyond the root node this paper presents a generic branching scheme in which the pricing oracle of the root node remains of use after branching assuming that the pricing oracle can handle bounds on the subproblem variables the scheme does not require the use of an extended formulation of the original problem it proceeds by recursively partitioning the subproblem solution set branching constraints are enforced in the pricing problem instead of being dualized via lagrangian relaxation and the pricing problem is solved by a limited number of calls to the pricing oracle this generic scheme builds on previously proposed approaches and unifies them we illustrate its use on the cutting stock and bin packing problems this is the first branch and price algorithm capable of solving such problems to integrality without modifying the subproblem or expanding its variable space

extending the bruhat order and the length function from the weyl group to the weyl monoid abstract for a symmetrizable kac moody algebra the category of admissible representations of the category o is an analogue of the category of finite dimensional representations of a semisimple lie algebra the monoid which is associated to this category and the category of restricted duals by a tannaka krein reconstruction contains the kac moody group as open dense unit group it has similar properties as a reductive algebraic monoid in particular there are bruhat and birkhoff decompositions the weyl group replaced by the weyl monoid c mokler an analogue of a reductive algebraic monoid whose unit group is a kac moody group arxiv math ag 0204246 mem amer math soc in press we determine the closure relations of the bruhat and birkhoff cells which give extensions of the bruhat order from the weyl group to the weyl monoid we show that the bruhat and birkhoff cells are irreducible and principal open in their closures we give product decompositions of the bruhat and birkhoff cells we define extended length functions which are compatible with the extended bruhat orders we show a generalization of some of the tits axioms for twin bn pairs

locally trivial principal homogeneous spaces and conjugacy theorems for lie algebras abstract we link locally trivial principal homogeneous spaces over spec r to the question of conjugacy of maximal abelian diagonalizable subalgebras of g r

automorphisms and isomorphisms of quantum generalized weyl algebras abstract we classify up to isomorphism the quantum generalized weyl algebras and determine their automorphism groups in all cases in a uniform way including the case where the parameter q is a root of unity thereby completing the results obtained by bavula and jordan 2001 5 and richard and solotar 2006 12

exact algorithm for minimising the number of setups in the one dimensional cutting stock problem the cutting stock problem is that of finding a cutting of stock material to meet demands for small pieces of prescribed dimensions while minimising the amount of waste because changing over from one cutting pattern to another involves significant setups an auxiliary problem is to minimise the number of different patterns that are used the pattern minimisation problem is significantly more complex but it is of great practical importance in this paper we propose an integer programming formulation for the problem that involves an exponential number of binary variables and associated columns each of which corresponds to selecting a fixed number of copies of a specific cutting pattern the integer program is solved using a column generation approach where the subproblem is a nonlinear integer program that can be decomposed into multiple bounded integer knapsack problems at each node of the branch and bound tree the linear programming relaxation of our formulation is made tighter by adding super additive inequalities branching rules are presented that yield a balanced tree incumbent solutions are obtained using a rounding heuristic the resulting branch and price and cut procedure is used to produce optimal or approximately optimal solutions for a set of real life problems

a characterization of certain loop lie algebras abstract in this paper we study z z graded lie algebras a i j z a i j with dim a i j 1 satisfying i dim dim 1 and is generated by ii sl iii 0 and ad act faithfully on we show that a is necessarily isomorphic to one of the two smallest loop algebras f t t 1 sl 2 and l 2 3 with appropriate grading

the nil hecke ring and cohomology of g p for a kac moody group g abstract let g be the group with borel subgroup b associated to a kac moody lie algebra unk with weyl group w and cartan subalgebra unk then h g b has among others four distinguished structures i an algebra structure ii a distinguished basis given by the schubert cells iii a module for w and iv a module for hecke type operators aw for w unk w we construct a ring r which we refer to as the nil hecke ring which is very simply and explicitly defined as a functor of w together with the w module unk alone and such that all these four structures on h g b arise naturally from the ring r

complete reducibility of subgroups of reductive algebraic groups over nonperfect fields 1 abstract let k be a nonperfect field of characteristic 2 let g be a k split simple algebraic group of type e 6 or g 2 defined over k in this paper we present the first examples of nonabelian non g completely reducible k subgroups of g which are g completely reducible over k our construction is based on that of subgroups of g acting non separably on the unipotent radical of a proper parabolic subgroup of g in our previous work we also present examples with the same property for a non connected reductive group g along the way several general results concerning complete reducibility over nonperfect fields are proved using the recently proved tits center conjecture for spherical buildings in particular we show that under mild conditions a connected k subgroup of g is pseudo reductive if it is g completely reducible over k

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

the cutting stock problem and integer rounding an integer programming problem is said to have the integer round up property if its optimal value is given by the least integer greater than or equal to the optimal value of its linear programming relaxation in this paper we prove that certain classes of cutting stock problems have the integer round up property the proof of these results relies upon the decomposition properties of certain knapsack polyhedra

conjugacy classes in affine kac moody groups and principal g bundles over elliptic curves abstract for a simple complex lie group g the connected components of the moduli space of semistable g bundles over an elliptic curve are weighted projective spaces or quotients of weighted projective spaces by a finite group action in this note we will provide a new proof of this result using the invariant theory of affine kac moody groups in particular the action of the twisted coxeter element on the root system of g

derivations and invariant forms of jordan and alternative tori jordan and alternative tori are the coordinate algebras of extended affine lie algebras of types a 1 and a 2 in this paper we show that the derivation algebra of a jordan torus is a semidirect product of the ideal of inner derivations and the subalgebra of central derivations in the course of proving this result we investigate derivations of the more general class of division graded jordan and alternative algebras we also describe invariant forms of these algebras

differential conformal superalgebras and their forms abstract we introduce the formalism of differential conformal superalgebras which we show leads to the correct automorphism group functor and accompanying descent theory in the conformal setting as an application we classify forms of n 2 and n 4 conformal superalgebras by means of galois cohomology

on dantzig wolfe decomposition in integer programming and ways to perform branching in a branch and price algorithm dantzig wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound the reformulation gives rise to an integer master problem whose typically large number of variables is dealt with implicitly by using an integer programming column generation procedure also known as branch and price algorithm there is a large class of integer programs that are well suited for this solution technique in this paper we propose to base the dantzig wolfe decomposition of an integer program on the discretization of the integer polyhedron associated with a subsystem of constraints as opposed to its convexification this allows us to formulate the integrality restriction directly on the master variables and sets a theoretical framework for dealing with specific issues such as branching or the introduction of cutting planes in the master we discuss specific branching schemes and their effect on the structure of the column generation subproblem we give theoretical bounds on the complexity of the separation process and the extent of the modifications to the column generation subproblem our computational tests on the cutting stock problem and a generalisation the cutting strip problem show that in practice all fractional solutions can be eliminated using branching rules that preserve the tractability of the subproblem but there is a trade off between branching efficiency and subproblem tractability

on the separation of maximally violated mod k cuts separation is of fundamental importance in cutting plane based techniques for integer linear programming ilp in recent decades a considerable research effort has been devoted to the definition of effective separation procedures for families of well structured cuts in this paper we address the separation of chvatal rank 1 inequalities in the context of general ilp s of the form min c t x ax b x integer where a is an m n integer matrix and b an m dimensional integer vector in particular for any given integer k we study mod k cuts of the form t ax t b for any 0 1 k k 1 k m such that t a is integer following the line of research recently proposed for mod 2 cuts by applegate bixby chvatal and cook 1 and fleischer and tardos 19 we restrict to maximally violated cuts i e to inequalities which are violated by k 1 k by the given fractional point we show that for any given k such a separation requires o mn min m n time applications to both the symmetric and asymmetric tsp are discussed in particular for any given k we propose an o v 2 e time exact separation algorithm for mod k cuts which are maximally violated by a given fractional symmetric or asymmetric tsp solution with support graph g v e this implies that we can identify a maximally violated cut for the symmetric tsp whenever a maximally violated extended comb inequality exists finally facet defining mod k cuts for the symmetric and asymmetric tsp are studied

parabolic kazhdan lusztig polynomials and schubert varieties abstract we shall give a description of the intersection cohomology groups of the schubert varieties in partial flag manifolds over symmetrizable kac moody lie algebras in terms of parabolic kazhdan lusztig polynomials introduced by deodhar

embedding of linear programming in a simulated annealing algorithm for solving a mixed integer production planning problem the present paper is concerned with the grouping of book covers on offset plates in order to minimize the total production cost the mathematical formulation of the problem involves both binary and continuous variables as exact methods are unable to provide solutions in reasonable time a heuristic algorithm of the simulated annealing type is proposed at each iteration the values of the current solution binary variables are altered in order to yield a neighboring solution to compute the corresponding values of the continuous variables and the value of the objective function a linear programming routine is called at each iteration this constitutes the main originality of the present approach and is in principle applicable in mixed integer programming problems the procedure is tested on several examples

one dimensional cutting stock problem to minimize the number of different patterns abstract as the cost associated with the change of cutting patterns become more important in recent industry we consider 1d csp in which the number of different cutting patterns is constrained within a given bound the proposed approach is based on metaheuristics and incorporates an adaptive pattern generation technique according to our computational experiments it is observed that the proposed algorithm provides comparable solutions to other existing heuristic approaches for 1d csp

a branch and cut and price algorithm for one dimensional stock cutting and two dimensional two stage cutting abstract the one dimensional cutting stock problem 1d csp and the two dimensional two stage guillotine constrained cutting problem 2d 2cp are considered in this paper the gilmore gomory models of these problems have very strong continuous relaxations providing a good bound in an lp based solution approach in recent years there have been several efforts to attack the one dimensional problem by lp based branch and bound with column generation called branch and price and by general purpose c hv a tal g omory cutting planes in this paper we investigate a combination of both approaches i e the lp relaxation at each branch and price node is strengthened by c hv a tal g omory and g omory mixed integer cuts the branching rule is that of branching on variables of the gilmore gomory formulation tests show that for 1d csp general purpose cuts are useful only in exceptional cases however for 2d 2cp their combination with branching is more effective than either approach alone and mostly better than other methods from the literature

tau functions and generalized integrable hierarchies the tau function formalism for a class of generalized zero curvature integrable hierarchies of partial differential equations is constructed the class includes the drinfel d sokolov hierarchies a direct relation between the variables of the zero curvature formalism and the tau functions is established the formalism also clarifies the connection between the zero curvature hierarchies and the hirotatype hierarchies of kac and wakimoto

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

irreducible cuspidal representations with prescribed local behavior let g be a simple algebraic group defined over the global field k in this paper we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of g with specified local behavior at a finite set of places of k and unramified elsewhere this sum is expressed as the product of the values of modified artin l functions at negative integers

a cohomological proof of peterson kacʼs theorem on conjugacy of cartan subalgebras for affine kac moody lie algebras abstract this paper deals with the problem of conjugacy of cartan subalgebras for affine kac moody lie algebras unlike the methods used by peterson and kac our approach is entirely cohomological and geometric it is deeply rooted on the theory of reductive group schemes developed by demazure and grothendieck and on the work of j tits on buildings

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

x inner automorphisms of semi commutative quantum algebras abstract many important quantum algebras such as quantum symplectic space quantum euclidean space quantum matrices q analogs of the heisenberg algebra and the quantum weyl algebra are semi commutative in addition enveloping algebras u l of even lie color algebras are also semi commutative in this paper we generalize work of montgomery and examine the x inner automorphisms of such algebras the theorems and examples in our paper show that for algebras r of this type the non identity x inner automorphisms of r tend to have infinite order thus if g is a finite group of automorphisms of r then the action of g will be x outer and this immediately gives useful information about crossed products r t g

deformations of lie algebras using σ derivations in this article we develop an approach to deformations of the witt and virasoro algebras based on sigma derivations we show that sigma twisted jacobi type identity holds for generators of such deformations for the sigma twisted generalization of lie algebras modeled by this construction we develop a theory of central extensions we show that our approach can be used to construct new deformations of lie algebras and their central extensions which in particular include naturally the q deformations of the witt and virasoro algebras associated to q difference operators providing also corresponding q deformed jacobi identities c 2005 elsevier inc all rights reserved

lattices of minimum covolume in chevalley groups over local fields of positive characteristic in this article we show that if g is a simply connected chevalley group of either classical type of rank bigger than 1 or type e6 and q 9 is a power of a prime number p 5 then g g fq t 1 up to an automorphism has a unique lattice of minimum covolume which is g fq t 1

computation of generalized equivariant cohomologies of kac moody flag varieties abstract in 1998 goresky kottwitz and macpherson showed that for certain projective varieties x equipped with an algebraic action of a complex torus t the equivariant cohomology ring h t x can be described by combinatorial data obtained from its orbit decomposition in this paper we generalize their theorem in three different ways first our group g need not be a torus second our space x is an equivariant stratified space along with some additional hypotheses on the attaching maps third and most important we allow for generalized equivariant cohomology theories e g instead of h t for these spaces we give a combinatorial description of e g x as a subring of e g f i where the f i are certain invariant subspaces of x our main examples are the flag varieties g p of kac moody groups g with the action of the torus of g in this context the f i are the t fixed points and e g is a t equivariant complex oriented cohomology theory such as h t k t or mu t we detail several explicit examples

the n component kp hierarchy and representation theory it is the aim of the present article to give all formulations of the n component kp hierarchy and clarify connections between them the generalization to the n component kp hierarchy is important because it contains many of the most popular systems of soliton equations like the davey stewartson system for n 2 the two dimensional toda lattice for n 2 the n wave system for n 3 and the darboux egoroff system it also allows us to construct natural generalizations to the davey stewartson and toda lattice systems of course the inclusion of all these systems in the n component kp hierarchy allows us to construct their solutions by making use of vertex operators

on conjugacy of cartan subalgebras in extended affine lie algebras abstract that finite dimensional simple lie algebras over the complex numbers can be classified by means of purely combinatorial and geometric objects such as coxeter dynkin diagrams and indecomposable irreducible root systems is arguably one of the most elegant results in mathematics the definition of the root system is done by fixing a cartan subalgebra of the given lie algebra the remarkable fact is that up to isomorphism this construction is independent of the choice of the cartan subalgebra the modern way of establishing this fact is by showing that all cartan subalgebras are conjugate for symmetrizable kac moody lie algebras with the appropriate definition of cartan subalgebra conjugacy has been established by peterson and kac an immediate consequence of this result is that the root systems and generalized cartan matrices are invariants of the kac moody lie algebras the purpose of this paper is to establish conjugacy of cartan subalgebras for extended affine lie algebras a natural class of lie algebras that generalizes the finite dimensional simple lie algebra and affine kac moody lie algebras

a loop group method for affine harmonic maps into lie groups we generalize the uhlenbeck segal theory for harmonic maps into compact semi simple lie groups to general lie groups equipped with torsion free bi invariant connection

covering algebras ii isomorphism of loop algebras this paper studies the loop algebras that arise from pairs consisting of a symmetrizable kac moody lie algebra g and a finite order automorphism of g we obtain necessary and sufficient conditions for two such loop algebras to be isomorphic

lie algebroids arising from simple group schemes abstract a classical construction of atiyah assigns to any real or complex lie group g manifold m and principal homogeneous g space p over m a lie algebroid over m 1 the spirit behind our work is to put this work within an algebraic context replace m by a scheme x and g by a simple reductive group scheme g over x in the sense of demazure grothendieck that arise naturally with an attached torsor which plays the role of p in the study of extended affine lie algebras see 9 for an overview lie algebroids in an algebraic sense were also considered by beilinson and bernstein we will explain how the present work relates to theirs

a characterization of the block lie algebra and itsq forms in characteristic 0 abstract the block algebra l referred to here is the lie algebra over a field f of characteristic 0 with basis e r s r s z z 0 0 and subject to the commutation relations e h k e r s rk sh e h r k s let 0 1 q f the q form l q of l is the lie algebra with basis e r s q r s z z 0 0 and subject to the commutation relations e h k q e r s q q rk q sh e h r k s q we study here a z z graded lie algebra formula with a 0 0 0 and dim a i j 1 for all i j z z 0 0 in this paper we show that a is necessarily isomorphic to l or l q l q l q for some q f if a satisfies a certain nondegeneracy condition

two dimensional representations of affine kac moody groups abstract we give a complete and explicit description for all two dimensional representations of non twisted affine kac moody groups those representations are found having a unique form characterized by homomorphisms between the base fields the homomorphisms from affine kac moody groups to two dimensional linear groups are also determined

a branch price and cut method for the vegetable crop rotation scheduling problem with minimal plot sizes abstract crop rotation plays an important role in agricultural production models with sustainability considerations commonly associated strategies include the alternation of botanical families in the plots the use of fallow periods and the inclusion of green manure crops in this article we address the problem of scheduling vegetable production in this context vegetables crop farmers usually manage a large number of crop species with different planting periods and growing times these crops present multiple and varied harvesting periods and productivities the combination of such characteristics makes the generation of good vegetable crop rotation schedules a hard combinatorial task we approach this problem while considering two additional important practical aspects standard plot sizes multiples of a base area and total area minimisation we propose an integer programming formulation for this problem and develop a branch price and cut algorithm that includes several performance enhancing characteristics such as the inclusion of a family of subadditive valid inequalities two primal heuristics and a strong branching rule extensive computational experiments over a set of instances based on real life data validate the efficiency and robustness of the proposed method

a geometric approach to complete reducibility let g be a connected reductive linear algebraic group we use geometric methods to investigate g completely reducible subgroups of g giving new criteria for g complete reducibility we show that a subgroup of g is g completely reducible if and only if it is strongly reductive in g this allows us to use ideas of r w richardson and hilbert mumford kempf from geometric invariant theory we deduce that a normal subgroup of a g completely reducible subgroup of g is again g completely reducible thereby providing an affirmative answer to a question posed by j p serre and conversely we prove that the normalizer of a g completely reducible subgroup of g is again g completely reducible some rationality questions and applications to the spherical building of g are considered many of our results extend to the case of non connected g

derivations of skew polynomial rings abstract let f be a field of characteristic 0 and let i j f for 1 i j n define r f x 1 x 2 x n to be the skew polynomial ring with x i x j i j x j x i and let s f x 1 x 2 x n x 11 x 12 x 1n be the corresponding laurent polynomial ring in a recent paper kirkman procesi and small considered these two rings under the assumption that s is simple and showed for example that the lie ring of inner derivations of s is simple furthermore when n 2 they determined the automorphisms of s related its ring of inner derivations to a certain block algebra and proved that every derivation of r is the sum of an inner derivation and a derivation which sends each xi to a scalar multiple of itself in this paper we extended these results to a more general situation specifically we study twisted group algebras ft g where g is a commutative group and f is a field of any characteristic furthermore we consider certain subalgebras ft h where h is a subsemigroup of g which generates g as a group finally if e g g f is a skew symmetric bilinear form then we study the lie algebra fe g associated with e and we consider its relationship to the lie structure defined on various twisted group algebras ft g

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

on cartan subalgebras abstract in this paper we study the concept of a cartan subalgebra in the context of locally finite and borcherds kac moody lie algebras

universal dependence on disorder of two dimensional randomly diluted and random bond j ising models we consider the two dimensional randomly site diluted ising model and the random bond j ising model also called the edwards anderson model and study their critical behavior at the paramagnetic ferromagnetic transition the critical behavior of thermodynamic quantities can be derived from a set of renormalization group equations in which disorder is a marginally irrelevant perturbation at the two dimensional ising fixed point we discuss their solutions focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder then we present a finite size scaling analysis of high statistics monte carlo simulations the numerical results confirm the renormalization group predictions and in particular the universality of the logarithmic corrections to the ising behavior due to quenched dilution

kac moody groups and integrability of soliton equations a new approach to integrability of affine toda field theories and closely related to them kdv hierarchies is proposed the flows of a hierarchy are explicity identified with infinitesimal action of the principal abelian subalgebra of the corresponding affine kac moody algebra on a homogeneous space

strong disorder paramagnetic ferromagnetic fixed point in the square lattice j ising model we consider the random bond j ising model on a square lattice as a function of the temperature t and of the disorder parameter p p 1 corresponds to the pure ising model we investigate the critical behavior along the paramagnetic ferromagnetic transition line at low temperatures below the temperature of the multicritical nishimori point at t 0 9527 1 p 0 89083 3 we present finite size scaling analyses of monte carlo results at two temperature values t 0 645 and t 0 5 the results show that the paramagnetic ferromagnetic transition line is reentrant for t t that the transitions are continuous and controlled by a strong disorder fixed point with critical exponents 1 50 4 0 128 8 and 0 095 5 this fixed point is definitely different from the ising fixed point controlling the paramagnetic ferromagnetic transitions for t t our results for the critical exponents are consistent with the hyperscaling relation 2 d 2 0

galois cohomology and forms of algebras over laurent polynomial rings 3 loop torsors 8 3 1 the witt tits index of a loop torsor 9 3 2 reducibility 12 3 3 almost commutative subgroups 14 3 4 almost commuting families of elements of finite order 16 3 5 almost commuting pairs and their invariants 17 3 6 failure in the anisotropic case 24

a note on bounding a class of linear programming problems including cutting stock problems in lp problems with an extremely large number of possible structural variables solution to optimality is not always required a bound can be used to terminate such lps such a bound is presented for a class of problem that includes most cutting stock formulations

the solution space of the unitary matrix model string equation and the sato grassmannian the space of all solutions to the string equation of the symmetric unitary one matrix model is determined it is shown that the string equation is equivalent to simple conditions on pointsv1 andv2 in the big cell gr 0 of the sato grassmannian gr this is a consequence of a well defined continuum limit in which the string equation has the simple form open image in new window matrices of differential operators these conditions onv1 andv2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation this geometric formulation leads directly to the virasoro constraintsln n 0 whereln annihilate the two modified kdv functions whose product gives the partition function of the unitary matrix model

infinite dimensional reductive monoids associated to highest weight representations of kac moody groups abstract starting with a highest weight representation of a kac moody group over the complex numbers we construct a monoid whose unit group is the image of the kac moody group under the representation multiplied by the nonzero complex numbers we show that this monoid has similar properties to those of a j irreducible reductive linear algebraic monoid in particular the monoid is unit regular and has a bruhat decomposition and the idempotent lattice of the generalized renner monoid of the bruhat decomposition is isomorphic to the face lattice of the convex hull of the weyl group orbit of the highest weight

lower bounds for essential dimensions via orthogonal representations let us first recall what is the essential dimension of a functor cf br 97 and r 00 let k be a field and let f be a functor from the category of field extensions of k into the category of sets let f k be an extension and let be an element of f f if e is a field with k e f we say that comes from e if it belongs to the image of f e f f the essential dimension ed of is the minimum of the transcendence degrees e k for all e with k e f such that comes from e one has ed tr deg f if there is equality we say that is incompressible the essential dimension ed f of f is ed f max ed the maximum being taken over all pairs f with k f and f f

multiloop realization of extended affine lie algebras and lie tori an important theorem in the theory of infinite dimensional lie algebras states that any affine kac moody algebra can be realized that is to say constructed explicitly using loop algebras in this paper we consider the corresponding problem for a class of lie algebras called extended affine lie algebras ealas that generalize affine algebras ealas occur in families that are constructed from centreless lie tori so the realization problem for ealas reduces to the realization problem for centreless lie tori we show that all but one family of centreless lie tori can be realized using multiloop algebras in place of loop algebras we also obtain necessary and sufficient conditions for two centreless lie tori realized in this way to be isotopic a relation that corresponds to isomorphism of the corresponding families of ealas

tits systems in a class of kac moody steinberg groups abstract the construction of the kac moody generalizations of the steinberg groups has not included the infinite dimensional versions of the great lie algebras this is because the construction has assumed the existence of representations with dominant integral highest weights an assumption which does not hold for those lie algebras an extension of the definition of the weyl group to the adjoint of the cartan subalgebra permits the construction of the steinberg groups with tits systems for that case

some forms of kac moody algebras let k be an algebraically closed field of char 0 the unique up to isomorphism three dimensional simple lie algebra s1 2 k plays an important role in the theory of the semisimple lie algebras over k for example chevalley harish chandra and serre s construction of the semisimple lie algebras g over k corresponding to a dynkin diagram 9 can be viewed as glueing together copies of sl 2 k in lf but we can not choose the distinct tds in an arbitrary way we need some compatibility conditions between the tds attached to neighbouring vertices they are described by some scalars sij and for simplicity we restrict our attention in this definition to dynkin diagrams without cycles for both definitions we also make the additional hypothesis that the

generic hecke algebra for renner monoids abstract to each renner monoid r we associate a generic hecke algebra h r over z q which is a deformation of the monoid z algebra of r if m is a finite reductive monoid with borel subgroup b and associated renner monoid r then we obtain the associated iwahori hecke algebra h m b by specialising q in h r and tensoring by c over z as in the classical case of finite reductive groups

invariants of real forms of affine kac moody lie algebras abstract the theory of vogan diagrams which are dynkin diagrams with an overlay of certain additional information allows one to give a rapid classification of finite dimensional real semisimple lie algebras and to make use of this classification in practice this paper develops a corresponding theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras in this case also the equivalence classes of vogan diagrams correspond to the isomorphism classes of almost compact real forms although the real forms of such algebras had already been classified the theory of vogan diagrams introduces invariants for such algebras and makes it possible to locate a given real form within the classification

actions of the face monoid associated to a kac moody group on its building abstract we described in c mokler an analogue of a reductive algebraic monoid whose unit group is a kac moody group mem amer math soc 823 2005 90 pp a monoid g acting on the integrable highest weight modules of a symmetrizable kac moody algebra it has similar structural properties as a reductive algebraic monoid with unit group a kac moody group g now we find natural extensions of the action of the kac moody group g on its building to actions of the monoid g on these extensions are partly motivated by representation theory and the combinatorics of the faces of the tits cone

torsors over the punctured affine line we provide a classification of g torsors over the punctured affine line rm spec k t pm 1 where g is a reductive algebraic group defined over a field k of good characteristic our classification is in terms of the galois cohomology of the complete field k t with values in g

τ functions and zero curvature equations of toda akns type the connection between functions and zero curvature equations for the homogeneous construction of the basic module l 0 over the simplest affine kac moody algebra a 1 1 is studied

pattern set generation algorithm for the one dimensional cutting stock problem with setup cost abstract the primary objective in the one dimensional cutting stock problem is to minimize material cost in real applications it is often necessary to consider auxiliary objectives one of which is to reduce the number of different cutting patterns setups this paper first presents an integer linear programming model to minimize the sum of material and setup costs over a given pattern set and then describes a sequential grouping procedure to generate the patterns in the set two sets of benchmark instances are used in the computational test the results indicate that the approach is efficient in improving the solution quality

quadratic spaces over laurent extensions of dedekind domains let abea dedekind domain in which 2 is invertible we show in this paper that any isotropic quadratic space over r t 7 1 is isometric to n ii q q hip with rank p n where if p denotes the hyperbolic space 1 some preliminary results in this section we prove some lemmas which will be used in the later sections we assume throughout the paper that in all the rings considered 2 is invertible if a q2 are quadratic spaces over r a j tq2 denotes the quadratic space a r r t t x l t a2 r r t t x over r t t x

infinite flag varieties and conjugacy theorems abstract we study the orbit of a highest weight vector in an integrable highest weight module of the group g associated to a kac moody algebra unk a we obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of unk a in particular we prove conjugacy theorems for cartan and borel subalgebras of unk a so that the cartan matrix a is an invariant of unk a

derivations of certain algebras defined by etale descent we give an explicit description of the lie algebra of derivations for a class of infinite dimensional algebras which are given by etale descent the algebras under consideration are twisted forms of central algebras over rings and include the multiloop algebras that appear in the construction of extended affine lie algebras

annihilating ideals of standard modules of rm sl 2 bbb c sp sim and combinatorial identities abstract introduction formal laurent series and rational functions generating fields the vertex operator algebra n k lambda 0 modules over n k lambda 0 relations on standard modules colored partitions leading terms and the main results colored partitions allowing at least two embeddings relations among relations relations among relations for two embeddings linear independence of bases of standard modules some combinatorial identities of rogers ramanujan type bibliography

theq virasoro like algebra abstract in this paper finite dimensional quotients of the q virasoro like algebra are determined when q is a root of unity as an application finite dimensional irreducible modules over the q virasoro like algebra are classified for any root q of unity

irreducible modules for extended affine lie algebras abstract we construct irreducible modules for twisted toroidal lie algebras and extended affine lie algebras this is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules we illustrate our method with examples of extended affine lie algebras of clifford type

geometric crystals on unipotent groups and generalized young tableaux abstract we define geometric unipotent crystal structure on maximal unipotent subgroups of semi simple algebraic groups we shall show that in a n case their ultra discretizations coincide with crystals obtained by generalizing young tableaux

generalized poisson brackets and lie algebras of type h in characteristic 0 the lie algebra of cartan type h which occurs as a subalgebra of the lie algebra of derivations of the polynomial algebra f x 1 dots x n x 1 dots x n was generalized by the first author to a class which included a subalgebra of the derivations of the laurent polynomials f x 1 dots x n x 1 dots x n x 1 1 dots x n 1 x 1 1 dots x n 1 we show in this paper that these generalizations of cartan type h algebras are isomorphic to certain generalizations of the classical algebra of poisson brackets and that it can be generalized further in turn these algebras can be recast in a form that is an adaption of a class of lie algebras of characteristic p that was defined in 1958 be r block a further generalization of these algebras is the main topic of this paper we show when these algebras are simple find their derivations and determine all possible isomorphisms between two of these algebras

automorphisms of toroidal lie superalgebras abstract we give a description of the algebraic group aut g of automorphisms of a simple finite dimensional lie superalgebra g over an algebraically closed field k of characteristic 0 which is obtained by viewing g as a module over a levi subalgebra of its even part as an application we give a detailed description of the group of automorphism of the k lie superalgebra g k r for a large class of commutative rings r