Non-locality of Equivariant Star Products on T∗(rp)
نویسنده
چکیده
Lecomte and Ovsienko constructed SLn+1(R)-equivariant quantization maps Qλ for symbols of differential operators on λ-densities on RP . We derive some formulas for the associated graded equivariant star products ⋆λ on the symbol algebra Pol(T ∗RP). These give some measure of the failure of locality. Our main result expresses (for n odd) the coefficients Cp(·, ·) of ⋆λ when λ = 1 2 in terms of some new SLn+1(C)-invariant algebraic bidifferential operators Zp(·, ·) on T ∗CP and the operators (E + n 2 ± s) where E is the fiberwise Euler vector field and s ∈ {1, 2, · · · , [ 2 ]}.
منابع مشابه
From Dixmier Algebras to Star Products
Let M be a Galois cover of a nilpotent coadjoint orbit of a complex semisimple Lie group. We define the notion of a perfect Dixmier algebra for M and show how this produces a graded (non-local) equivariant star product on M with several very nice properties. This is part of a larger program we have been developing for working out the orbit method for nilpotent orbits.
متن کاملEquivariant Deformation Quantization for the Cotangent Bundle of a Flag Manifold
Let XR be a (generalized) flag manifold of a non-compact real semisimple Lie group GR, where XR and GR have complexifications X and G. We investigate the problem of constructing a graded star product on Pol(T ∗XR) which corresponds to a GR-equivariant quantization of symbols into smooth differential operators acting on half-densities on XR. We show that any solution is algebraic in that it rest...
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملInvolutions Fixing Rp
This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space RP with its normal bundle nonbounding and a Dold manifold P (h, i) with h > 0 and i > 0. For odd h, the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of P (h,...
متن کاملTopological Types of 3-dimensional Small Covers
In this paper we study the (equivariant) topological types of a class of 3dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a (Z2) -action such that its orbit space is a simple convex 3-polytope. We introduce six equivariant operations on such 3-dimensional closed manifolds. These six operations are interesting because of their combinatorial natures. Then we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000