Trilinear alternating forms on a vector space of dimension 7

Alternating Trilinear Forms and Groups of Exponent

The theory of alternating bilinear forms on finite dimensional vector spaces V is well understood; two forms on V are equivalent if and only if they have equal ranks. The situation for alternating trilinear forms is much harder. This is partly because the number of forms of a given dimension is not independent of the underlying field and so there is no useful canonical description of an alterna...

On Canonical Binary Trilinear Forms

On the Structure of Bounded Trilinear Forms

0. Introduction. In previous work CKP1], CKP2] the authors have initiated a study of Schatten-von Neumann classes of trilinear forms in Hilbert space. We believe however that, in order to progress further, it is necessary to gain a better understanding of the structure of bounded forms, and of compact ones. This is a rather intricate problem. Accordingly, in this paper we have collected various...

Quaternary binary trilinear forms

Dear friends, In 1997 or 1998 I began to write a paper [20], trying to extend the known description of binary forms of norm unity, in the real or complex cases, to the case of quaternions, but I never finished it. In 2002, I resumed my work but then I was unable to understand what I had done, so I made a fresh start with somewhat different assumptions. Now I have realized that this was a gross ...

Conformally invariant trilinear forms on the sphere

To each complex number λ is associated a representation πλ of the conformal group SO0(1, n) on C∞(Sn−1) (spherical principal series). For three values λ1, λ2, λ3, we construct a trilinear form on C∞(Sn−1)×C∞(Sn−1)×C∞(Sn−1), which is invariant by πλ1 ⊗πλ2 ⊗ πλ3 . The trilinear form, first defined for (λ1, λ2, λ3) in an open set of C is extended meromorphically, with simple poles located in an ex...