Asociación, discriminación y Constitución: los límites entre la autonomía asociativa y el derecho de los socios —y aspirantes a serlo— a no ser discriminados

Este artículo tiene por objeto el análisis de la relación entre el derecho de los socios a su auto-organización interna, sin injerencias procedentes de los poderes públicos, y el derecho de estos mismos socios —y aspirantes a serlo— a no ser discriminados en su relación con la asociación. Así como el principio democrático ha sido aceptado como un límite legal frente al derecho a la auto-organización interna, los derechos de los socios —y aspirantes a serlo— en su relación inter privatos con la asociación forman también parte, según el TC, del contenido esencial del derecho de asociación y, por tanto, limitan la capacidad autoorganizativa de la asociación. Entre estos derechos se sitúan la imposibilidad de la no admisión o la expulsión de socios por causas arbitrarias, injustificadas, entre las que, en opinión del autor, se deben encuadrar aquellas que se basen en los rasgos especialmente odiosos que señala la Constitución, como la raza o el género, cuando dichos rasgos nada tengan que ver con la finalidad de la asociación. En todo caso, los Tribunales deberán hacer una ponderación, caso a caso, entre el art. 22 CE en su dimensión auto-organizativa y el art. 22 CE en su dimensión inter privatos en coordinación con el art. 14 CE, sin que una posible futura previsión legal prohibiendo las prácticas discriminatorias pudieran tacharse de inconstitucional.This article analyses the relationship between the rights of the members of an association to self-organization without interferences from the State, and the rights of the members—and those who want to be members—to not be discriminated against in their connection to the association. As the democratic principle has been accepted as a legal limit to internal self-organization, the rights of the members and those who want to be members in their relationship inter privatos with the association are part of the essential content of the right to association, according to the Constitutional Court. Therefore, they limit the selforganization of the association. Among these rights we find the right to stop an arbitrary non admission and expulsion of members. The author thinks that members have the right to stop a non admission or expulsion based on race, gender or other grounds that are deemed as especially hateful by Constitution as part of their rights inter privatos, but only if the goal of the association doesn’t justify the use of these grounds. In the end, the Courts might find a balance, case by case, between article 22 CE (right to association) in their self-organizational dimension and art. 22 CE (right to association) in their inter privatos dimension in connection with the article 14 CE (right to equality). But if any law forbids the discrimination in the future, it will be constitutional

Small representations of finite classical groups

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimensions tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of important conjectures which are currently out of reach. Despite the classification by Lusztig of the irreducible representations of finite groups of Lie type, it seems that this aspect remains obscure. In this note we develop a language which seems to be adequate for the description of the "small" representations of finite classical groups and puts in the forefront the notion of rank of a representation. We describe a method, the "eta correspondence", to construct small representations, and we conjecture that our construction is exhaustive. We also give a strong estimate on the dimension of small representations in terms of their rank. For the sake of clarity, in this note we describe in detail only the case of the finite symplectic groups.Comment: 18 pages, 9 figures, accepted for publications in the proceedings of the conference on the occasion of Roger Howe's 70th birthday (1-5 June 2015, Yale University, New Haven, CT

Generalized Gauss Maps and Integrals for Three-Component Links: Toward Higher Helicities for Magnetic Fields and Fluid Flows

To each three-component link in the 3-sphere we associate a generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. We view this as a natural extension of the familiar situation for two-component links in 3-space, where the linking number is the degree of the classical Gauss map from the 2-torus to the 2-sphere. The generalized Gauss map, like its prototype, is geometrically natural in the sense that it is equivariant with respect to orientation-preserving isometries of the ambient space, thus positioning it for application to physical situations. When the pairwise linking numbers of a three-component link are all zero, we give an integral formula for the triple linking number analogous to the Gauss integral for the pairwise linking numbers. This new integral is also geometrically natural, like its prototype, in the sense that the integrand is invariant under orientation-preserving isometries of the ambient space. Versions of this integral have been applied by Komendarczyk in special cases to problems of higher order helicity and derivation of lower bounds for the energy of magnetic fields. We have set this entire paper in the 3-sphere because our generalized Gauss map is easiest to present here, but in a subsequent paper we will give the corresponding maps and integral formulas in Euclidean 3-space

Generalized Gauss Maps and Integrals for Three-Component Links: Toward Higher Helicities for Magnetic Fields and Fluid Flows

To each three-component link in the 3-sphere we associate a generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. We view this as a natural extension of the familiar situation for two-component links in 3-space, where the linking number is the degree of the classical Gauss map from the 2-torus to the 2-sphere. The generalized Gauss map, like its prototype, is geometrically natural in the sense that it is equivariant with respect to orientation-preserving isometries of the ambient space, thus positioning it for application to physical situations. When the pairwise linking numbers of a three-component link are all zero, we give an integral formula for the triple linking number analogous to the Gauss integral for the pairwise linking numbers. This new integral is also geometrically natural, like its prototype, in the sense that the integrand is invariant under orientation-preserving isometries of the ambient space. Versions of this integral have been applied by Komendarczyk in special cases to problems of higher order helicity and derivation of lower bounds for the energy of magnetic fields. We have set this entire paper in the 3-sphere because our generalized Gauss map is easiest to present here, but in a subsequent paper we will give the corresponding maps and integral formulas in Euclidean 3-space