Non-Locality of Equivariant Star Products on T*(RPⁿ)

Original · EN

Lecomte and Ovsienko constructed SLₙ₊₁(R)-equivariant quantization maps Qλ for symbols of differential operators on λ-densities on ⁿ. We derive some formulas for the associated graded equivariant star products starλ on the symbol algebra Pol(T*ⁿ). These give some measure of the failure of locality. Our main result expresses (for n odd) the coefficients Cₚ of starλ when λ= in terms of some new SLₙ₊₁(C)-invariant algebraic bidifferential operators Zₚ on T*ⁿ and the operators (E+n/2± s)⁻¹ where E is the fiberwise Euler vector field and s∈{1,2,...,[p/2]}.