Related papers: Integration over compact quantum groups

We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…

A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We develop the theory completely within the von Neumann algebra framework. At various points, we also do…

A fundamental property of compact groups and compact quantum groups is the existence and uniqueness of a left and right invariant probability -- the Haar measure. This is a natural playground for classical and quantum probability, provided…

Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…

We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their co-adjoint orbits. The sufficient condition for the contractability of a representation is expressed via cocycles on coadjoint…

This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…

We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…

Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Given a Lie group $G$, a compact subgroup $K$ and a representation $\tau\in\hat K$, we assume that the algebra of $\text{End}(V_\tau)$-valued, bi-$\tau$-equivariant, integrable functions on $G$ is commutative. We present the basic facts of…

We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…

We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…

Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…

Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz' approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of $q$ being an~odd root of unity. Here we find the~irreducible representations for all…

A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated.…

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure,…

We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…

Using the multi-parametric deformation of the algebra of functions on $ \GL{n+1} $ and the universal enveloping algebra $ \U{\igl{n+1}} $, we construct the multi-parametric quantum groups $ \IGLq{n} $ and $ \Uq{\igl{n}} $.