Related papers: Function Theory in the Quantum Matrix Ball: an Inv…
An operator theoretic approach to invariant integration theory on non-compact quantum spaces is introduced on the example of the quantum (n,1)-matrix ball O_q(Mat_{n,1}). In order to prove the existence of an invariant integral, operator…
We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see…
We have introduced q-analogues of bounded symmetric domains in our work q-alg/9703005. Given the simplest ones among those, the works q-alg/9603012 and math.QA/9803110 announce the relations describing the algebras of functions,…
This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…
In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of those results is related to the invariance of kernels of…
In the paper we find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
The maximum principle for holomirphic functions in the quantum ball is formulated. A proof can be found in [8] (see the bibliography).
We introduce the quantum $j$-invariant in positive characteristic as a multi-valued, modular-invariant function of a local function field. In this paper, we concentrate on basic definitions and questions of convergence. Note: This version…
We introduce two new sets of invariant functions of quark mass matrices, which express the constraints on these mass matrices due to knowledge of the quark mixing matrix. These invariants provide a very simple method to test candidate forms…
Plancherel formula is one of the celebrated result of harmonic analysis on semisimple Lie groups and their homogeneous spaces. The main goal of this work is to find a q-analog of the Plancherel formula for spherical transform the unit…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
Our previous work (math.QA/9808015) introduces the basic notions and announces some results on function theory in the quantum disc. The present paper establishes a relationship between those results and the quantum groups theory.
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
A sketch of a recent approach to quantum gravity is presented which involves several unconventional aspects. The basic ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach for…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
The functional integral has many triumphs in elucidating quantum theory. But incorporating charge fractionalization into that formalism remains a challenge.
An integral transform for G=U(1,q) is studied. The transform maps the positive spin ladder representations of G on a Bargmann-Segal-Fock space F_n^1,q into a space of polynomial-valued functions on the bounded realization B^q of G/K. An…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.