Littlewood-Richardson Coefficients via Yang-Baxter Equation

The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain scattering matrix that satisfies a Yang-Baxter type equation. The corresponding piecewise-linear transformations of parameters give a solution to the tetrahedron equation. These transformation maps are naturally related to the dual canonical bases for modules over the quantum enveloping algebra $U_q(sl_n)$. A byproduct of our construction is an explicit description for the cone of Kashiwara's parametrizations of dual canonical bases. This solves a problem posed by Berenstein and Zelevinsky. We present a graphical interpretation of the scattering matrices in terms of web functions, which are related to honeycombs of Knutson and Tao.Comment: 24 page

Gilberto Bosques y el consulado de México en Marsella (1940-1942). La burocracia en tiempos de guerra

ResumenA partir de fuentes de archivo inéditas, el artículo complejiza el papel que desempeñaron el cónsul mexicano Gilberto Bosques y el Consulado de México en Marsella, entre 1940 y 1942, en relación al salvamento de refugiados europeos (no españoles). Se analiza el papel fundamental que desempeñaron los grupos de ayuda para conseguir las visas para los refugiados, el funcionamiento burocrático del consulado y el hecho de que cientos de visas no fueron entregadas a sus destinatarios debido a la imposición de requisitos imposibles de cumplir. Mientras que la memoria popular recuerda a Bosques trabajando en la excepción, las fuentes históricas consultadas lo retratan trabajando en la normalidad de la burocracia mexicana: una normalidad que aparece desvinculada del contexto de guerra y persecución que la rodeaba.AbstractBased on unpublished archive sources, this paper examines in depth the role played by Mexican consul Gilberto Bosques and the Mexican Consulate in Marseille between 1940 and 1942, in relation to the rescue of European (non-Spanish) refugees. The fundamental role played by assistance groups in obtaining visas for refugees is analyzed, as well as the bureaucratic operation of the consulate and the fact that hundreds of visas were not delivered to their recipients, due to the imposition of demands that were impossible to meet. While collective memory sees Bosques as working in a state of exception, the historical sources consulted portray him working in normal conditions of Mexican bureaucracy: a normality that appears detached from the surrounding context of war and persecution

Some Explicit Solutions of the Additive Deligne-Simpson Problem and Their Applications (Preprint)

In this paper we construct three infinite series and two extra triples of complex matrices B, C, and A=B+C of special spectral types associated to C. Simpson's classification in his paper ``Products of Matrices'' and a classification of multiple flag varieties with finitely many orbits of the diagonal action of the general linear group by P. Magyar, J. Weyman, and A. Zelevinsky. This enables us to construct Fuchsian systems of differential equations which generalize the hypergeometric equation of Gauss-Riemann. In a sense, they are the closest relatives of the famous equation, because their triples of spectral flags have finitely many orbits of the diagonal action of the general linear group in the space of solutions. We also construct a scalar product such that A, B, and C are self-adjoint with respect to it. In the context of Fuchsian systems, this scalar product becomes a monodromy invariant complex symmetric bilinear form in the space of solutions. When the eigenvalues of A, B, and C are real, the matrices and the scalar product become real as well. We find inequalities on the eigenvalues of A, B, and C which make the scalar product positive-definite. As proved by A. Klyachko, the spectra of three hermitian (or real symmetric) matrices B, C, and A=B+C form a polyhedral convex cone in the space of triple spectra. He also gave a recursive algorithm to generate inequalities describing the cone. The inequalities we obtain describe non-recursively some faces of the Klyachko cone

Geographies of hope: reflections on the creation of the Museum of Climate Hope

Amid growing concerns about climate anxiety in young people, researchers and practitioners in climate change education (CCE) have called for pedagogies of hope. The Museum of Climate Hope emerged from interdisciplinary conversations at the University of Oxford about creative approaches to CCE in both formal and informal educational settings. This article explores the geographical aspects of this initiative, from the physical experience of walking a museum trail across Oxford to the digital experience of ArcGIS StoryMaps linking stories of climate resilience, innovation and transformation across time and space

Semigroups of sl3(C)sl_3(\mathbb{C}) tensor product invariants

We compute presentations for a family of semigroup algebras related to the problem of decomposing $sl_3(\mathbb{C})$ tensor products. Along the way we find new toric degenerations of the Grassmannian variety $Gr_3(\mathbb{C}^n)$ which $T-$invariant for $T \subset GL_n(\mathbb{C})$ the diagonal torus.Comment: 12 pages, 13 figure

Las relaciones entre México y el Tercer Reich, 1933-1941

Este texto analiza las relaciones germano-mexicanas durante el nazismo, desde 1933 hasta el rompimiento de relaciones diplomáticas en 1941. A diferencia de la historiografía sobre el tema —que se centra primordialmente en los intereses germanos hacia América Latina— la intención es analizar ambas partes de la ecuación, dando una especial consideración a los intereses mexicanos hacia Alemania. Después de años de intentar acrecentar sus relaciones comerciales, fue la nacionalización del petróleo mexicano en 1938 la que finalmente ocasionaría una cooperación económica más cercana entre los dos países. Cuando esta fue interrumpida por el comienzo de la guerra, las diferencias políticas, minimizadas una y otra vez a lo largo de los años treinta, adquirirían un peso primordial