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

2000/10/27 by Ranee Brylinski, Brylinski, Ranee
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.QA #math.SG

paper · pdf · doi:10.48550/arxiv.math/0010259

6 pages

arxiv created 2000/10/27 · arxiv updated 2009/11/30

Abstract

Lecomte and Ovsienko constructed SL_n+1(R)-equivariant quantization maps Q_λ for symbols of differential operators on λ-densities on \RPⁿ. We derive some formulas for the associated graded equivariant star products star_λ 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 star_λ when λ=\half 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)]\.

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