Projectively Equivariant Quantization and Symbol calculus in dimension 1|2

Najla Mellouli (1)

1 ICJ - Institut Camille Jordan

The spaces of higher-order differential operators (in Dimension 1|2), which are modules over the stringy Lie superalgebra K(2), are isomorphic to the corresponding spaces of symbols as orthosymplectic modules in non resonant cases. Such an osp (2|2)-equivariant quantization, which has been given in second-order differential operators case, keeps existing and unique. We calculate its explicit formula that provides extension in particular order cases.

Mots clés: Equivariant quantization; conformal superalgebra

Domaines: Physique mathématique [math-ph]; Géométrie différentielle [math.DG]; Algèbres quantiques [math.QA]; Théorie des représentations [math.RT]; Physique mathématique [math-ph]

Najla Mellouli. Projectively Equivariant Quantization and Symbol calculus in dimension 1|2. 2011. ⟨hal-00603186⟩