We show that the special case of Serre duality involved in the Borel-Bott-Weil theorem can be formulated and proved in the context of equi-variant Kasparov theory by combining the Atiyah-Singer index theorem and the framework of equivariant correspondences developed in another paper by the first author and Ralf Meyer. The twisted Dolbeault cohomology groups of a flag variety that figure in the ...

We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed ŝl(2) affine Lie algebra symmetry of the sine-Gordon theory can be used to derive the S-matrices of the Φ perturbations of the minimal unitary series. This analysis provides an identification of fields which create the massive kink spectrum. ...

Here we take the view that small abelian categories are certain categorical versions of rings and the collection of Serre subcategories of a small abelian category is then analogous to the set of ideals of a commutative ring. We consider two topologies on the collection of Serre subcategories; one is a very direct lift of the Zariski topology, the other, dual, topology appeared in the context o...