arXiv subjects

Omar Saldarriaga

Publications and source records attributed to Omar Saldarriaga.

4 recordsLinked to original sources

arXiv2018

New Characterization of Flat Affine Manifolds and the Associative Envelope of a Left Symmetric Algebra

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection. Then we specialize the characterization to the case of a left invariant connection on a Lie group. In the last case, we show the existence of a Lie group endowed with a flat affine bi-invariant connection whose Lie algebra contains the Lie algebra of complete infinitesimal affine transformations of the given Lie group. We also prove some results about flat affine manifolds whose group of diffeomorphisms admit a flat affine bi-invariant structure. The paper is illustrated with several examples.

math.DG↗

arXiv2016

Flat Affine or Projective Geometries on Lie Groups

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results determine Lie groups admitting flat bi-invariant affine or projective structures. These groups could play an essential role in the study of homogeneous spaces $M=G/H$ admitting flat affine or flat projective structures invariant under the natural action of $G$ on $M$. A. Medina asked several years ago if the group of affine transformations of a flat affine Lie group is a flat projective Lie group. In this work we provide a partial possitive answer to this question.

math.DG↗

arXiv2011

A particular case of the Level increasing Conjecture for Type A fusion algebras

A particular case of the level increasing conjecture for type A fusion coefficientes is proved for when one the weights is a multiple of the first fundamental weight.

math.RT↗

arXiv2004

Fusion algebras, symmetric polynomials, orbits of N-groups, and rank-level duality

A method of computing fusion coefficients for Lie algebras of type $A_{n-1}$ on level $k$ was recently developed by A. Feingold and M. Weiner \cite{FW} using orbits of $\mathbb{Z}_n^k$ under the permutation action of $S_k$ on $k$-tuples. They got the fusion coefficients only for n = 2 and 3. We will extend this method to all $n \geq 2$ and all $k \geq 1$. First we show a connection between Young diagrams and $S_k$-orbits of $\mathbb{Z}_n ^k$, and using Pieri rules we prove that this method works for certain specific weights that generate the fusion algebra. Then we show that the orbit method does not work in general, but with the help of the Jacobi-Trudi determinant, we give an iterative method to reproduce all type A fusion products.

math.RA↗