Seminarium i Talteori och Algebraisk Geometri

Abstrakt finns endast på engelska: We discuss an interesting story relating the orthosymplectic Howe dual pair osp(n|2),so(D) inside osp(nD|2D) to classical massless spin n/2 fields, freely propagating in D-dimensional flat spacetime with D>2. The Lorentz algebra so(D) (and its (super)conformal extension) is contained in a larger algebra, called the reduction algebra, which acts on the solution space to the field equations. One can use this to explicitly write down all polynomial solutions. For spins 0, 1/2, and 1, we also computed presentations of the reduction algebras by generators and relations, using the extremal projector method and the double coset realization. In ongoing work, we add to this sequence the spin 3/2 case of a vector-spinor whose field equation is the Rarita-Schwinger equation describing the gravitino. The spin 2 case should be related to linearized gravity.

I will strive to make the first part of my talk (pre-seminar) accessible to a broad audience.

The talk is based in part on joint work with L. Uhl, D. Williams, and M. Dorang.