相关论文: Quantum matrix ball: the Bergman kernel

We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin…

This volume contains a mildly expanded version of lectures and talks at seminars and conferences, as well as review papers on subjects listed in the title of the volume. A great deal of these texts have already been published or sent to…

Can a dynamically robust (\textit{aka} stable) $Q$-ball reproduce the rotation curve of a disk galaxy? In an astrophysical environment, $Q$-balls are non-topological solitons that are transparent and only perceived by their gravitational…

The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…

A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the…

In the paper we consider the polyharmonic Bergman space for the union of the rotated unit Euclidean balls. Using so called zonal polyharmonics we derive the formulas for the kernel of this space. Moreover, we study the weighted polyharmonic…

The main focus of this contribution is on the harmonic Bergman spaces $\mathcal{B}_{\alpha}^{p}$ on the $q$-homogeneous tree $\mathfrak{X}_q$ endowed with a family of measures $\sigma_\alpha$ that are constant on the horocycles tangent to a…

In this article, we prove the transformation formula for the reduced Bergman kernels under proper holomorphic correspondences between bounded domains in the complex plane. As a corollary, we obtain the transformation formula for the reduced…

We explore the indecomposable submodule structure of quantum Grassmann super-algebra $\Omega_q(m|n)$ and its truncated objects $\Omega_q(m|n,\textbf{r})$ in the case when $q=\varepsilon$ is an $\ell$-th root of unity. A net-like…

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

The natural generalization of the notion of bundle in quantum geometry is that of bimodule. If the base space has quantum group symmetries one is particularly interested in bimodules covariant (equivariant) under these symmetries. Most…

We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.

This paper studies the quotient geometry of bounded or fixed-rank correlation matrices. We establish a bijection between the set of bounded-rank correlation matrices and a quotient set of a spherical product manifold by an orthogonal group.…

On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the…

This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…

A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…

Coquasitriangular universal ${\cal R}$ matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects…