Graphical introduction to classical Lie algebras

We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary and easy to handle and, thus provides an effective tool for computations with classical Lie algebras. More over, it may be regarded as a first and foundational step in the process of uncovering the categorical meaning of Lie algebras.Comment: 28 pages, 68 figure

On the q-meromorphic Weyl algebra

We introduce a q-analogue MW_q for the meromorphic Weyl algebra, and study the normalization problem and the symmetric powers sym^n(MW_q) for such algebra from a combinatorial viewpoint.Comment: Final Version, 14 pages, 1 figur

Symmetric quantum Weyl algebras

We study the symmetric powers of four algebras: $q$-oscillator algebra, $q$-Weyl algebra, $h$-Weyl algebra and $U({\mathfrak {sl}}_2)$. We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.Comment: To appear in the Annales Mathematiques Blaise Pasca

Quantum Product of Symmetric Functions

We provide an explicit description of the quantum product of multisymmetric functions using the elementary multisymmetric functions introduced by Vaccarino

Sobre el álgebra de Weyl q-meromórfica

Presentamos un q analógico MWq para el merylorphic Weyl álgebra, y estudia el problema de normalización y las potencias simétricas Symn (MWq) para tal álgebra desde un punto de vista combinatorioWe introduce a q-analogue MWq for the meromorphic Weyl algebra, and study the normalization problem and the symmetric powers Symn (MWq) for such algebra from a combinatorial viewpoint