finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

generalized kahler potentials from supergravity we consider supersymmetric mathcal n 2 solutions with non vanishing ns three form building on worldsheet results we reduce the problem to a single generalized monge ampere equation on the generalized kahler potential k recently interpreted geometrically by lindstrom rocek von unge and zabzine one input in the procedure is a holomorphic function w that can be thought of as the effective superpotential for a d3 brane probe the procedure is hence likely to be useful for finding gravity duals to field theories with non vanishing abelian superpotential such as leigh strassler theories we indeed show that a purely ns precursor of the lunin maldacena dual to the deformed mathcal n 4 super yang mills falls in our class

groupe de chow de codimension deux des varietes definies sur un corps de nombres un theoreme de finitude pour la torsion letx be a smooth projective variety defined over a number field and let ch2 x denote the chow group of codimension two cycles modulo rational equivalence we show that if the cohomology grouph2 x ox vanishes then the torsion subgroup of ch2 x is a finite group this result covers all previous results in this direction the hypothesish2 x ox 0 is used to lift line bundles

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

generalized complex geometry generalized complex geometry encompasses complex and symplectic ge ometry as its extremal special cases we explore the basic properties of this geometry including its enhanced symmetry group elliptic deforma tion theory relation to poisson geometry and local structure theory we also dene and study generalized complex branes which interpolate be tween at bundles on lagrangian submanifolds and holomorphic bundles on complex submanifolds

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

quantum twisted yangians symmetry baxterisation and centralizers based on the quantum twisted yangians integrable systems with special boundary conditions called soliton nonpreserving snp may be constructed in the present article we focus on the study of subalgebras of the quantum twisted yangians and we show that such a subalgebra provides an exact symmetry of the rational transfer matrix we discuss how the spectrum of a generic transfer matrix may be obtained by focusing only on two types of special boundaries it is also shown that the subalgebras emerging from the asymptotics of tensor product representations of the quantum twisted yangian turn out to be dual to the quantum brauer algebra to deal with general boundaries in the trigonometric case we propose a new algebra which also provides the appropriate framework for the baxterisation procedure in the snp case

contracted and expanded integrable structures we propose a generic framework to obtain certain types of contracted and centrally extended algebras this is based on the existence of quadratic algebras reflection algebras and twisted yangians naturally arising in the context of boundary integrable models a quite old misconception regarding the expansion of the e2 algebra into sl2 is resolved using the representation theory of the aforementioned quadratic algebras we also obtain centrally extended algebras associated with rational and trigonometric q deformed r matrices that are solutions of the yang baxter equation

perturbing gauge gravity duals by a romans mass we show how to produce algorithmically gravity solutions in massive iia as infinitesimal first order perturbations in the romans mass parameter dual to assigned conformal field theories we illustrate the procedure on a family of chern simons matter conformal field theories that we recently obtained from the theory by waiving the condition that the levels sum up to zero

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

gersten s conjecture for thek theory with torsion coefficients of a discrete valuation ring between quillen k groups induced by the obvious inclusion functors are all zero in 6 quillen proved this conjecture if r is essentially of finite type over a field in the case of discrete valuation rings this conjecture reduces to conjecture let r be a discrete valuation ring with residue field k and field of fractions f then for all q z 0 the transfer map which is defined since every k vector space is of finite projective dimension as an r module k k k r is zero equivalently the map r ec f induced by the ring homomorphism r p f is injective a third equivalent formulation is that the boundary map

eigenvalues of casimir invariants of uq gl m n a method is investigated for determining the eigenvalues of the casimir invariants of the quantum supergroup uq gl m n when acting on irreducible highest weight representations this leads to a simple eigenvalue formula expressible in terms of the highest weight labels

fock representations of the affine lie algebra a 1 1 the aim of this note is to show that the affine lie algebraa1 1 has a natural family v of fock representations on the spacec xi yj i andj parametrized by v c2 by corresponding the highest weight of to each the parameter spacec2 forms a double cover of the weight spacec 0 c 1 with singularities at linear forms of level 2 this number is 1 times the dual coxeter number our results contain explicit realizations of irreducible non integrable highest wieghta1 1 modules for generic v

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

quantum spin chain with soliton non preserving boundary conditions we consider the case of an integrable quantum spin chain with soliton non preserving boundary conditions this is the first time that such boundary conditions have been considered in the spin chain framework we construct the transfer matrix of the model we study its symmetry and we find explicit expressions for its eigenvalues moreover we derive a new set of bethe ansatz equations by means of the analytical bethe ansatz method

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

boundary k matrices for the six vertex and the n 2n 1 an 1 vertex models boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices k or theta for the six vertex model the general solution depending on four arbitrary parameters is found for the an 1 models all diagonal solutions are found the associated integrable magnetic hamiltonians are explicitly derived

isomorphism of two realizations of quantum affine algebra u_q widehat mathfrak g mathfrak l text n text we establish an explicit isomorphism between two realizations of the quantum affine algebra u q widehat mathfrak g mathfrak l text n text given previously by drinfeld and reshetikhin semenov tian shansky our result can be considered as an affine version of the isomorphism between the drinfield jimbo and the faddeev reshetikhin takhtajan constructions of the quantum algebra u q mathfrak g mathfrak l n

casimir operators of uq sl 3 the q deformed casimir operators of u sl 3 are constructed using the hopf algebra structure and the fundamental representation of uq sl 3

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

generalised g 2 manifolds we define new riemannian structures on 7 manifolds by a differential form of mixed degree which is the critical point of a possibly constrained variational problem over a fixed cohomology class the unconstrained critical points generalise the notion of a manifold of holonomy g 2 while the constrained ones give rise to a new geometry without a classical counterpart we characterise these structures by means of spinors and show the integrability conditions to be equivalent to the supersymmetry equations on spinors in type ii supergravity theory with bosonic background fields in particular this geometry can be described by two linear metric connections with skew symmetric torsion finally we construct explicit examples by introducing the device of t duality

some splitting results in the k theory of rings ii for all n 3 0 the main cases in which the conjecture is known to be valid are the equicharacteristic case 7 based on 2 and the case in which k is finite or more generally algebraic over a finite field 2 lo in a related vein gillet has recently proved that the conjecture is valid for k theory with coefficients in z m so long as m 1 char k 3 in s we showed that the sequence above is actually split exact whenever r contains a field l such that k is a finite separable extension of l or whenever r is henselian and k is finite the main result of this note is that the henselian hypothesis in the latter case is unnecessary