Negative-dimensional groups in quantum physics

The author shows that an explicit definition of negative-dimensional classical groups in terms of their action on Grassmann representation spaces, together with Weyl's character formula for the Grassmann tensorial representations of such groups, leads to a framework in which some surprising 'negative-dimensional' properties of group theoretic invariants arise naturally. As an application, he shows that the spectra of the Grassmann harmonic oscillator and of Grassmann angular momentum are related to their bosonic counterparts by a simple analytic continuation in the dimension.