19 citations · 98 across the 26 of their papers we have counts for
23 papers · 1 filter
Formal oscillatory distributions
Alexander Karabegov
We introduce the notion of an oscillatory formal distribution supported at a point. We prove that a formal distribution is given by a formal oscillatory integral if and only if it…
An algebra of distributions related to a star product with separation of variables
Alexander Karabegov
Given a star product with separation of variables on a pseudo-Kähler manifold and a point , we construct an associative algebra of formal distributions suppo…
Formal oscillatory integrals and deformation quantization
Alexander Karabegov
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point of the phase f…
A heat kernel proof of the index theorem for deformation quantization
Alexander Karabegov
We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canon…
Deformation quantization with separation of variables on a super-Kähler manifold
Alexander Karabegov
We construct deformation quantizations with separation of variables on a split super-Kähler manifold and describe their canonical supertrace densities.
On the phase form of a deformation quantization with separation of variables
Alexander Karabegov
Given a star product with separation of variables on a pseudo-Kaehler manifold, we obtain a new formal (1,1)-form from its classifying form and call it the phase form of the star p…
Deformation quantization with separation of variables of an endomorphism bundle
Alexander Karabegov
Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomor…
On Gammelgaard's formula for a star product with separation of variables
Alexander Karabegov
We show that Gammelgaard's formula expressing a star product with separation of variables on a pseudo-Kaehler manifold in terms of directed graphs without cycles is equivalent to a…
An invariant formula for a star product with separation of variables
Alexander Karabegov
We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.
An explicit formula for a star product with separation of variables
Alexander Karabegov
For a star product with separation of variables * on a pseudo-Kaehler manifold we give a simple closed formula of the total symbol of the left star multiplication operator L_f by a…
Star products with separation of variables admitting a smooth extension
Alexander Karabegov
Given a complex manifold with an open dense subset endowed with a pseudo-Kaehler form which cannot be smoothly extended to a larger open subset, we consider various exa…
Infinitesimal deformations of a formal symplectic groupoid
Alexander Karabegov
Given a formal symplectic groupoid over a Poisson manifold , we define a new object, an infinitesimal deformation of , which can be thought of as a formal symplect…
A mapping from the unitary to doubly stochastic matrices and symbols on a finite set
Alexander V. Karabegov
We prove that the mapping from the unitary to the doubly stochastic matrices that maps a unitary matrix (u_{kl}) to the doubly stochastic matrix (|u_{kl}|^2) is a submersion for al…
A formal model of Berezin-Toeplitz quantization
Alexander V. Karabegov
We give a new construction of symbols of the differential operators on the sections of a quantum line bundle over a Kaehler manifold using the natural contravariant connect…
Deformation quantization of a Kaehler-Poisson structure vanishing on a Levi nondegenerate hypersurface
Alexander V. Karabegov
We give an elementary proof of the result by Leichtnam, Tang, and Weinstein that there exists a deformation quantization with separation of variables on a complex manifold endowed…
Fedosov's formal symplectic groupoids and contravariant connections
Alexander V. Karabegov
Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In…
Formal symplectic groupoid of a deformation quantization
Alexander V. Karabegov
We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal sym…
On the inverse mapping of the formal symplectic groupoid of a deformation quantization
Alexander V. Karabegov
To each natural star product on a Poisson manifold we associate an antisymplectic involutive automorphism of the formal neighborhood of the zero section of the cotangent bundle…
On Dequantization of Fedosov's Deformation Quantization
Alexander V. Karabegov
To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to th…
A covariant Poisson deformation quantization with separation of variables up to the third order
Alexander Karabegov
We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a Kähler manifold M. Unlike C_1 and C_2, this operator can no…
Almost Kaehler deformation quantization
Alexander V. Karabegov, Martin Schlichenmaier
We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformati…
Identification of Berezin-Toeplitz deformation quantization
Alexander V. Karabegov, Martin Schlichenmaier
We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformatio…
On Fedosov's approach to deformation quantization with separation of variables
Alexander V. Karabegov
The description of all deformation quantizations with separation of variables on a Kaehler manifold obtained in our earlier paper is used to identify the Fedosov star-product of Wi…