Related papers: The Haar State on SU_q(N)
We compute the mapping class group action on cycles on the configuration space of the torus with one puncture, with coefficients in a local system arising in conformal field theory. This action commutes with the topological action of the…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group $G$ with its…
We show the existence and uniqueness of a massless supersymmetric ground state wavefunction of a SU(2) matrix model in a bounded smooth domain with Dirichlet boundary conditions. This is a gauge system and we provide a new framework to…
We apply the Tannaka-Krein duality theory for quantum homogeneous spaces, developed in the first part of this series of papers, to the case of the quantum SU(2) groups. We obtain a classification of their quantum homogeneous spaces in terms…
A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these…
Using face algebras (i.e. algebras of L-operators of IRF models), we construct modular tensor categories with positive definite inner product, whose fusion rules and S-matrices are the same as (or slightly different from) those obtained by…
The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring.…
We give two examples of algebras of differential operators associated to families of matrix valued orthogonal polynomials arising from representations of SU$(N+1)$. The first one gives a commutative algebra and the second one a…
Given a quadratic two-parameter matrix polynomial in Newton basis $Q_{N} (\lambda ,\mu)$, we construct a vector space of linear two-parameter matrix polynomials and identify a set of linearizations which lie in the vector space. We also…
We investigate non-commutative gauge theories in homogeneous spaces G/H. We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G. The isometry of a homogeneous space, G must be a…
The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an…
From SUSY ladder operators in momentum space of a neutron in the magnetic field of a linear current, we construct $2\times 2$ matrix operators that together with the z-component of the angular momentum satisfy the su(2) Lie algebra. We use…
Explicit expressions for associated spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables.
We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…
An extended Hubbard model with phonons is considered. q-coherent states relative to the superconducting quantum symmetry of the model are constructed and their properties studied. It is shown that they can have energy expectation lower than…
We obtain a $q$-analog of a well known Sahi result on the joint spectrum of $S(GL_n \times GL_n)$-invariant differential operators with polynomial coefficients on the vector space of complex $n \times n$-matrices.
The generalized coherent states for quantum groups introduced by Jurco and Stovicek are studied for the simplest example SU_q(2) in full detail. It is shown that the normalized SU_q(2) coherent states enjoy the property of completeness, and…
The posibility of quantizing the anomalous $SU(N)$ Yang--Mills model preserving the symmetry under the orthogonal subgroup is indicated. The corresponding Wess--Zumino action (1-cocycle) possesses the additional $SO(N)$ symmetry and can be…
Horn functions form a subclass of Boolean functions possessing interesting structural and computational properties. These functions play a fundamental role in algebra, artificial intelligence, combinatorics, computer science, database…