Nonlocality of Equivariant Star Products on T*( RPn)

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