Newton polytopes and symmetric Grothendieck polynomials

Symmetric Grothendieck polynomials are inhomogeneous versions of Schur polynomials that arise in combinatorial $K$-theory. A polynomial has saturated Newton polytope (SNP) if every lattice point in the polytope is an exponent vector. We show Newton polytopes of these Grothendieck polynomials and their homogeneous components have SNP. Moreover, the Newton polytope of each homogeneous component is a permutahedron. This addresses recent conjectures of C. Monical-N. Tokcan-A. Yong and of A. Fink-K. M\'esz\'aros-A. St. Dizier in this special case.Comment: 4 pages, 1 figur

K-orbit closures and Barbasch-Evens-Magyar varieties

We define the Barbasch-Evens-Magyar variety. We show it is isomorphic to the smooth variety defined in [D. Barbasch-S. Evens '94] that maps finite-to-one to a symmetric orbit closure, thereby giving a resolution of singularities in certain cases. Our definition parallels [P. Magyar '98]'s construction of the Bott-Samelson variety [H. C. Hansen '73, M. Demazure '74]. From this alternative viewpoint, one deduces a graphical description in type A, stratification into closed subvarieties of the same kind, and determination of the torus-fixed points. Moreover, we explain how these manifolds inherit a natural symplectic structure with Hamiltonian torus action. We then prove that the moment polytope is expressed in terms of the moment polytope of a Bott-Samelson variety.Comment: 26 pages, 4 figure

Three-body problem in 3D space: ground state, (quasi)-exact-solvability

We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories in the classical case are of this type. The quantum (and classical) system for which these states are eigenstates is found and its Hamiltonian is constructed. It corresponds to a three-dimensional quantum particle moving in a curved space with special metric. The kinetic energy of the system has a hidden $sl(4,R)$ Lie (Poisson) algebra structure, alternatively, the hidden algebra $h^{(3)}$ typical for the $H_3$ Calogero model. We find an exactly solvable three-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable three-body sextic polynomial type potential; both models have an extra integral.Comment: 24 pages, Appendix about non-equal masses adde

Törless, la amistad y el homoerotismo: una mirada desde las asociaciones políticas, el espacio y el poder

En este artículo se hace un análisis de la obra Las tribulaciones del estudiante Törless, escrita por el autor austriaco Robert Musil -- El concepto de la amistad constituye uno de los ejes centrales de este texto, de manera que se pretende hacer un análisis de esta relación entendida como un tipo de institución política en el que las acciones generales son movilizadas esencialmente por actos y experiencias particulares que obedecen a disentimientos y relaciones asimétricas producto de la situación de control, basadas en la normatividad institucional, la subjetividad y el saber, entendidos desde Foucault como sistemas de poder que regulan la práctica de la sexualidad y la forma en que los individuos pueden reconocerse como sujetos de una(s) sexualidad(es) -- Tal sexualidad, evidentemente, está minada y problematizada por la moralidad que da lugar a lo que el mismo Foucault denomina estéticas de la existencia y técnicas del sí, entendidas como “las prácticas sensatas y voluntarias por las que los hombres no sólo se fijan reglas de conducta, sino que buscan transformarse a sí mismos, modificarse en su ser singular y hacer de su vida una obra que presenta ciertos valores estéticos y responde a ciertos criterios de estilo” -- En ese sentido, del estudio de la amistad a través de autores como Aristóteles se derivan interpretaciones relacionadas con el vínculo ente cuerpo y espacio (Bachelard, Carus, Todorov) en los procesos de desarrollo de los personajes (Bremond), especialmente del joven Törles

SYNTESIS AND CRYSTALLINE STRUCTURE OF THE EXO-3,6-DIMETHYL-3,6-EPOXI-1,2,3,6-TETRAHYDROPHTLALIMIDE AND ITS N-BROMODECYL ANALOG: TWO THERMALLY LABILE DIELS-ALDER ADDUCTS

Indexación: Web of Science; Scielo.The molecular structure of the exo-3,6-dimethyl-3,6-epoxi-1,2,3,6-tetrahydrophthalimide (1), determined by X-ray diffraction analysis, as well as, its complete spectroscopic characterization and the synthesis and complete spectroscopic characterization of its N-(10-bromodecyl) analog (2) are presented.http://ref.scielo.org/kh5xv

Particular Integrability and (Quasi)-exact-solvability

A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland Hamiltonians for all roots are found. In the classical case some special trajectories for which the corresponding particular constants of motion appear are indicated.Comment: 13 pages, typos correcte