Projectively equivariant quantizations over the superspace ${\mathbb{R}}^{p|q}$

Abstract

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.

19 pages

References in corpus (5)

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Cited by in corpus (7)

• Natural and Projectively Invariant Quantizations on Supermanifolds
• On osp(p+1,q+1|2r)-equivariant quantizations
• spo(2|2)-Equivariant Quantizations on the Supercircle $S^{1|2}$
• Conformally equivariant quantization and symbol maps associated with $n$-ary differential operators on weighted densities
• On the matrix realization of the Lie superalgebra of contact projective vector fields $\mathfrak{spo}(2l+2|n)$
• Heisenberg order of differential operators on the superspaces ${\mathbb{R}}^{2l+1|n}$
• The fine $\spo(2|n)$-equivariant quantizations on the super circles $S^{1|n}$