On certain modules of covariants in exterior algebras

We study the structure of the space of covariants $B:=\left(\bigwedge (\mathfrak g/\mathfrak k)^*\otimes \mathfrak g\right)^{\mathfrak k},$ for a certain class of infinitesimal symmetric spaces $(\mathfrak g,\mathfrak k)$ such that the space of invariants $A:=\left(\bigwedge (\mathfrak g/\mathfrak k)^*\right)^{\mathfrak k}$ is an exterior algebra $\wedge (x_1,...,x_r),$ with $r=rk(\mathfrak g)-rk(\mathfrak k)$. We prove that they are free modules over the subalgebra $A_{r-1}=\wedge (x_1,...,x_{r-1})$ of rank $4r$. In addition we will give an explicit basis of $B$. As particular cases we will recover same classical results. In fact we will describe the structure of $\left(\bigwedge (M_n^{\pm})^*\otimes M_n\right)^G$, the space of the $G-$equivariant matrix valued alternating multilinear maps on the space of (skew-symmetric or symmetric with respect to a specific involution) matrices, where $G$ is the symplectic group or the odd orthogonal group. Furthermore we prove new polynomial trace identities.Comment: Title changed. Results have been generalised to other infinitesimal symmetric space

Linear semigroups with coarsely dense orbits

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit contains a coarsely dense subset of some open cone $C$ in $V$ then the closure of the orbit contains the closure of $C$. In the complex case the orbit is then actually dense in $V$. For the real case we give precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page

On Motives Associated to Graph Polynomials

The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions.Comment: 54

Berry phase in homogeneous K\"ahler manifolds with linear Hamiltonians

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of {\em classical} objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.Comment: LaTeX fil

A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark

Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament

Elevages caprins en Guadeloupe

Une enquête a été réalisée dans 120 élevages par l'INRA-CRAAG afin de déterminer les caractéristiques de l'élevage local et ses potentialités. Les données sont exploitées selon des techniques classiques d'analyse multidimensionnelle aboutissant à une description des différents paramètres de l'exploitation guadeloupéenne et à une typologie des élevages. L'élevage caprin présente certaines originalités : spéculation fréquemment associée à l'élevage bovin permettant une exploitation variable selon les systèmes d'une large diversité de ressources (savanes naturelles, prairies plantées et parcours) auxquelles s'ajoutent différents aliments apportés en compléments et les fourrages issus de la "fauche sauvage". Cet élevage apparaît comme un moyen d'intensification, d'augmentation du produit "socio-économique" de l'exploitation agricole. Certains éleveurs choisissent de mettre en place des structures semi-intensives d'élevage. La pratique du pâturage tournant est proposée. Cependant, la pratique de l'élevage au piquet reste très vivace et serait un moyen de résoudre pour certains éleveurs le problème du foncie

Análise genética do início do florescimento em feijoeiro pelo "Triple Test Cross".

objetivo deste trabalho foi detectar a presença de epistasia e estimar os componentes da variância genética para o caráter início do florescimento em populações de feijoeiro (Phaseolus vulgaris L.) oriundas de genitores de diferentes conjuntos gênicos (pools gênicos)

Potencial de populações segregantes de feijoeiro oriundas de cruzamentos intra e inter conjuntos gênicos.

Esse trabalho teve como objetivo comparar o potencial de populações segregantes de feijoeiro oriundas do cruzamento de genitores de mesmo conjunto gênico e de conjuntos gênicos diferentes por meio de estimativas de alguns parâmetros genéticos e fenotípicos