Related papers: Tensor Operators for Uh(sl(2))
An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures…
A realization of various algebraic structures in terms of the $C_{\lambda}$-extended oscillator algebras is introduced. In particular, the $C_{\lambda}$-extended oscillator algebras realization of Fairlie-Fletcher-Zachos (FFZ)algebra is…
An exact Jordan-Wigner type of transformation is presented in 1D connecting spin-1/2 operators to spinful canonical Fermi operators. The transformation contains two free parameters allowing a broad interconnection possibility in between…
We present a general derivation of semi-fermionic representation for generators of SU(N) group as a bilinear combination of Fermi operators. The constraints are fulfilled by means of imaginary Lagrange multipliers. The important case of…
We provide a uniform construction of $L^2$-models for all small unitary representations in degenerate principal series of semisimple Lie groups which are induced from maximal parabolic subgroups with abelian nilradical. This generalizes…
We construct explicit differential operators on hermitian modular forms, extending methods developed for Siegel modular forms. These differential operators are closely related to the two-variable spherical pluriharmonic polynomials. We…
Let $u_1,\ldots,u_n$ be unitary operators on a Hilbert space $H$. We study the norm $$\left\|\sum^{i=n}_{i=1} u_i \otimes \bar u_i\right\|\leqno (1)$$ of the operator $\sum u_i \otimes \bar u_i$ acting on the Hilbertian tensor product…
Recently, an algebraic generalization of the Jordan-Wigner transformation was introduced and applied to one- and two-dimensional systems. This transformation is composed of the interactions $\eta_{i}$ that appear in the Hamiltonian ${\cal…
Given a free module L over a commutative ring k, we study two k-linear operators on the tensor algebra of T(L): One of them sends a pure tensor u_1 (X) u_2 (X) ... (X) u_k to the sum of all tensors u_i (X) u_1 (X) u_2 (X) ... (X) (skip u_i)…
The work is devoted to a probably new connection between deformed Virasoro algebra and quantum $\widehat{\mathfrak{sl}}_2$. We give an explicit realization of Virasoro current via vertex operators of level 1 integrable representation of…
Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result.…
The q-oscillator representation for the Borel subalgebra of the affine symmetry $U_q(sl_N^)$ is presented. By means of this q-oscillator representation, we give the free field realizations of the Baxter's Q-operator $Q_j(t)$, $\bar{Q}_j(t)$…
We propose a theory of $\lambda$-tensor product of operator spaces which extends the theory of Blecher-Paulsen and Effros-Ruan for the operator space projective tensor product \cite{blecp}, \cite{effros}, \cite{eff} and that of…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…
We present a set of BRST invariant composite operators in the $SU\left(2\right)\times U\left(1\right)$ Higgs model which exhibit an overlap with the observable scalar and vector particle states of the theory. Some of these operators are…
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\hat {\frak sl}(2))$…
Four apparently different bosonizations of the $U_q(su(2)_k)$ quantum current algebra for arbitrary level $k$ have recently been proposed in the literature. However, the relations among them have so far remained unclear except in one case.…
We give the Heisenberg realization for the quantum algebra $U_q(sl_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(sl_n)$ on the $q$-symmetric algebra $A_q(Mat_n)$ by the…
After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a…
We give a detailed description of the resolution of the identity of a second order $q$-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The $q$-difference operator and the two choices of…