Upcoming talks:
Jonas Hartwig (Iowa State University)
November 18, 2025
Title: Higher spin fields and orthosymplectic reduction algebras
Abstract: 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. The Lorentz algebra so(D) (and its (super)conformal extension) is contained in a larger algebra, called the reduction algebra (or hypersymmetry algebra), which acts on the solutions space to the field equations. One can use this to explicitly write down all polynomial solutions. We also computed presentations of these reduction algebras by generators and relations, using the extremal projector method and the double coset realization. Spins 0, 1/2, 1 correspond respectively to scalar, Dirac spinor, and vector fields. 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 accessible to a broad audience.
The talk is based in part on joint work with Lillian Ryan Uhl, Dwight Anderson Williams II, and Matthew Tyler Dorang.
Past talks:
Lisa Carbone (Rutgers University)
October 31, 2024
Title: Symmetry Groups in Infinite Dimensions
Abstract: The study of many physical theories requires an understanding of symmetries of infinite dimensional Lie algebras. The construction of groups of automorphisms for infinite dimensional Lie algebras is challenging, but there is a well established theory for the class of Kac-Moody algebras. A generalization of Kac-Moody algebras known as Borcherds algebras arise in string theory models, but the methods for constructing Kac-Moody groups break down for this more general class. We discuss the challenges that arise and describe several approaches to constructing groups for Borcherds algebras. Our main example is the Monster Lie algebra which plays an important role in the solution of Monstrous Moonshine and which is a symmetry algebra of a model of the compactified Heterotic String.