arXiv subjects
Publications and source records attributed to Rafael Díaz.
We build a continuous analogue for Young diagrams, thought of as left-aligned stairs, following the line of research initiated by Díaz and Cano on the construction of continuous analogues for combinatorial objects.
We develop continuous analogues for the Pochhammer symbol following the line of research initiated by Díaz and Cano on the construction of continuous analogues for combinatorial objects.
We give a combinatorial interpretation for the hypergeometric functions associated with tuples of rational numbers.
We introduce the concept of $N$-differential graded algebras (N-dga), and study the moduli space of deformations of the differential of a N-dga. We prove that it is controlled by what we call the N-Maurer-Cartan equation.
We consider deformations of the differential of a $q$-differential graded algebra. We prove that it is controlled by a generalized Maurer-Cartan equation. We find explicit formulae for the coefficients $c_k$ involved in that equation.
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on shell action, which are area-invariants. A geometrical interpretation of these invariants is given.
We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.