Tensorial Forms in Infinite Dimensions

Let V be a complex vector space and consider symmetric d-linear forms on V, i.e., linear maps Symd(V)→>C. When V is finite dimensional and d>2, the structure of such forms is very complicated. Somewhat surprisingly, when V has countably infinite dimension there is much more order. For instance, there is a unique isomorphism class of form that is ultrahomogeneous (joint work with N. Harman), and (at least for d=3) it is possible to classify forms up to a notion of isogeny (joint work with A. Danelon). This circle of ideas is closely related to the notion of strength of polynomials, and also to the geometry of polynomial representations.



Andrew Snowden


University of Michigan