Almost-Kähler Deformation Quantization

We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kähler manifold which respects the almost-Kähler structure in order to construct a Fedosov-type deformation quantization on this manifold.     

An invariant formula for a star product with separation of variables

We give an invariant formula for a star product with separation of variables on a pseudo-Kähler manifold.     

On the Canonical Normalization of a Trace Density of Deformation Quantization

We describe a procedure of the canonical normalization of a formal trace density of an arbitrary deformation quantization on a symplectic manifold. We apply this procedure to give an explicit expression of the canonical formal trace density of deformation quantization with separation of variables on a pseudo-Käahler manifold.     

Generalized operator-valuedpq-symbols and geometric quantization

Joint Institute for Nuclear Research, Dubna. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 2, pp. 76–79, April–June, 1995.     

A heat kernel proof of the index theorem for deformation quantization

Letters in Mathematical Physics - We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kähler manifold. We use...     

Berezin's quantization on flag manifolds and spherical modules

We show that the theory of spherical Harish-Chandra modules naturally gives rise to Berezin's symbol quantization on generalized flag manifolds. It provides constructions of symbol algebras and of their representations for covariant and contravariant symbols, and also for symbols which so far have no explicit definition. For all these symbol algebras we give a general proof of the correspondence principle.