Diagram automorphisms and quantum groups

Diagram Automorphisms and Rank-level Duality

We study the effect of diagram automorphisms on rank-level duality. We create new symplectic rank-level dualities from T. Abe’s symplectic rank-level duality on genus zero smooth curves with marked points and chosen coordinates. We also show that ranklevel dualities for the pair sl(r), sl(s) in genus 0 arising from representation theory can also be obtained from the parabolic strange dualities ...

Modular Groups, Visibility Diagram and Quantum Hall Effect

We consider the action of the modular group Γ(2) on the set of positive rational fractions. From this, we derive a model for a classification of fractional (as well as integer) Hall states which can be visualized on two “visibility” diagrams, the first one being associated with even denominator fractions whereas the second one is linked to odd denominator fractions. We use this model to predict...

Some properties of marginal automorphisms of groups

AbstractLet W be a non-empty subset of a free group. The automorphism of a group G is said to be a marginal automorphism, if for all x in G,x^−1alpha(x) in W^*(G), where W^*(G) is the marginal subgroup of G.In this paper, we give necessary and sufficient condition for a purelynon-abelian p-group G, such that the set of all marginal automorphismsof G forms an elementary abelian p-group.

Groups with unifoml automorphisms

Matroid Automorphisms And Symmetry Groups

For a subgroup W of the hyperoctahedral group On which is generated by reflections, we consider the linear dependence matroid MW on the column vectors corresponding to the reflections in W . We determine all possible automorphism groups of MW and determine when W ∼= Aut(MW ). This allows us to connect combinatorial and geometric symmetry. Applications to zonotopes are also considered. Signed gr...