Related papers: $R$ Matrix for $U_{q}E_{7}$
In this paper we give a detailed classification scheme for three-dimensional quantum zero curvature representation and tetrahedron equations. This scheme includes both even and odd parity components, the resulting algebras of observables…
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…
The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study…
We give explicit expression of recurrency formulae of canonical realization for quantum enveloping algebras $U_{q}(sl(n+1,C))$. In these formulas the generators of the algebra $U_{q}(sl(n+1,C))$ are expressed by means of n-canonical q-boson…
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…
We establish an explicit algebra isomorphism between the quantum reflection algebra for the $U_q(\hat{sl_2})$ R-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal…
The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping…
A reduced-density-matrix (RDM)-based approach to {\em ab initio} cavity quantum electrodynamics (QED) is developed. The expectation value of the Pauli-Fierz Hamiltonian is expressed in terms of one- and two-body electronic and photonic…
Modified universal R-matrices, associated with the central extension (through the Drinfeld's double construction) of the quantum groups U_q(sl_n), are realized through an infinite dimensional spectral parameter dependent solution for the…
In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin $R$-matrix is associated with the affine quantum algebra $U_q(\widehat{sl(2)})$. The…
We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B$, $C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix…
We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.
We list characters (one-dimensional representations) of the reflection equation algebra associated with the fundamental vector representation of the Drinfeld-Jimbo quantum group $\U_q\bigl(gl(n)\bigr)$.
Infinite dimensional representations of the real form U_q(u_{n,1}) of the Drinfeld--Jimbo algebra U_q(gl_{n+1}) are defined. The principal series of representations of U_q(u_{n,1}) is studied. Intertwining operators for pairs of the…
Explicit formulas of the universal $R$-matrix are given for all quantized nontwisted rank 3 affine Lie algebras $U_q(A_2^{(1)})\,,~U_q(C_2^{(1)})$ and $U_q(G_2^{(1)})$.
This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent…
Let $\g$ be a complex orthogonal or symplectic Lie algebra and $\g'\subset \g$ the Lie subalgebra of rank $\rk \g'=\rk \g-1$ of the same type. We give an explicit construction of generators of the Mickelsson algebra $Z_q(\g,\g')$ in terms…
In the present paper we are dealing with reflection equation algebras ${\cal L}(R)$ corresponding to even skew-invertible Hecke symmetries. Our main result consists in computing the characters of the spectral values of the generating matrix…
Let ${U}_q(sl_2)$ be the quantized enveloping algebra associated to the simple Lie algebra $sl_2$. In this paper, we study the quantum double $D_q$ of the Borel subalgebra ${U}_q((sl_2)^{\leq 0})$ of ${U}_q(sl_2)$. We construct an analogue…
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…