196 research outputs found
Classification of polarized deformation quantizations
We give a classification of polarized deformation quantizations on a
symplectic manifold with a (complex) polarization. Also, we establish a formula
which relates the characteristic class of a polarized deformation quantization
to its Fedosov class and the Chern class of the polarization.Comment: 40 pages, AMS Late
Quantum G-manifolds
Let be a Lie group, \g its Lie algebra, and U_h(\g) the corresponding
quantum group. We consider some examples of U_h(\g)-invariant one and two
parameter quantizations on -manifolds.Comment: Latex2e, 13 pp. A talk at the workshop "New homological and
categorical methods in mathematical physics", Manchester, July 5-12, 200
Double quantization of \cp type orbits by generalized Verma modules
It is known that symmetric orbits in for any simple Lie algebra
are equiped with a Poisson pencil generated by the
Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to
the "canonical" R-matrix. We realize quantization of this Poisson pencil on
\cp type orbits (i.e. orbits in whose real compact form is ) by means of q-deformed Verma modules.Comment: 21 pages, LaTeX, no figure
Quantum symmetric spaces
Let be a semisimple Lie group, its Lie algebra. For any
symmetric space over we construct a new (deformed) multiplication in
the space of smooth functions on . This multiplication is invariant
under the action of the Drinfeld--Jimbo quantum group and is
commutative with respect to an involutive operator . Such a multiplication is unique. Let be a k\"{a}hlerian
symmetric space with the canonical Poisson structure. Then we construct a
-invariant multiplication in which depends on two parameters
and is a quantization of that structure.Comment: 16 pp, LaTe
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