Supertransvectants and symplectic geometry

Hichem Gargoubi (1) , Valentin Ovsienko (2)

1 IPEIT - Institut Préparatoire aux Etudes d'Ingénieur de Tunis
2 ICJ - Institut Camille Jordan

We consider the $osp(1|2)$-invariant bilinear operations on weighted densities on the supercircle $S^{1|1}$ called the supertransvectants. These operations are analogues of the famous Gordan transvectants (or Rankin-Cohen brackets). We prove that these operations coincide with the iterated Poisson and ghost Poisson brackets on ${\mathbb R}^{2|1}$ and apply this result to construct star-products involving the supertransvectants.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Géométrie symplectique [math.SG]; Théorie des représentations [math.RT]

Hichem Gargoubi, Valentin Ovsienko. Supertransvectants and symplectic geometry. 2008. ⟨hal-00145402v2⟩