相关论文: Integration over compact quantum groups
Given a Hecke symmetry $R$, one can define a matrix bialgebra $E_R$ and a matrix Hopf algebra $H_R$, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to $R$. We show that for an even…
This article provides a concise introduction to the theory of Haar measures on locally compact Hausdorff groups. We cover the necessary preliminaries on topological groups and measure theory, the Haar correspondence, unimodularity and Haar…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…
In the general theory of locally compact quantum groups, the notion of Haar measure (Haar weight) plays the most significant role. The aim of this paper is to carry out a careful analysis regarding Haar weight, in relation to general…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…
This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic…
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.
The quantum spectral curve equation associated to KP $\tau$-functions of hypergeometric type serving as generating functions for rationally weighted Hurwitz numbers is solved by generalized hypergeometric series. The basis elements spanning…
In this article, we develop a theory of integration on algebraic quantum groupoids in the form of regular multiplier Hopf algebroids, and establish the main properties of integrals obtained by Van Daele for algebraic quantum groups before -…
In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra $\mathcal{T}$. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual…
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…