Differential operators on supercircle: conformally equivariant quantization and symbol calculus
Gargoubi, Hichem ; Mellouli, Najla ; Ovsienko, Valentin
HAL, hal-00109286 / Harvested from HAL
Text on HAL
We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra $K(1)$ acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the Möbius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist.
Publié le : 2006-10-30
Classification:  Equivariant quantization,  superconformal algebra,  MSC 53D55, 17B68, 17B10,  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],  [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] 
@article{hal-00109286,
     author = {Gargoubi, Hichem and Mellouli, Najla and Ovsienko, Valentin},
     title = {Differential operators on supercircle: conformally equivariant quantization and symbol calculus},
     journal = {HAL},
     volume = {2006},
     number = {0},
     year = {2006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00109286}
}

Gargoubi, Hichem; Mellouli, Najla; Ovsienko, Valentin. Differential operators on supercircle: conformally equivariant quantization and symbol calculus. HAL, Tome 2006 (2006) no. 0, . http://gdmltest.u-ga.fr/item/hal-00109286/