相关论文: A note on $q$-oscillator realizations of $U_{q}(gl…
We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U_q(gl(M|N)) in the…
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 $Q_j(t)$, $\bar{Q}_j(t)$…
The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The…
We consider intertwining relations of the augmented $q$-Onsager algebra introduced by Ito and Terwilliger, and obtain generic (diagonal) boundary $K$-operators in terms of the Cartan element of $U_{q}(sl_2)$. These $K$-operators solve…
In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gl(n+1) and so(2n+1). Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in…
We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N=1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the…
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…
{Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we…
Explicit expressions for the generators of the quantum superalgebra $U_q[gl(n/m)]$ acting on a class of irreducible representations are given. The class under consideration consists of all essentially typical representations: for these a…
A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag…
Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.
We provide an alternative approach to the Faddeev-Reshetikhin-Takhtajan presentation of the quantum group U_q(g), with L-operators as generators and relations ruled by an R-matrix. We look at U_q(g) as being generated by the quantum Borel…
We show that our construction of realizations for Lie algebras and quantum algebras can be generalized to quantum superalgebras, too. We study an example of quantum superalgebra $U_q(gl(2/1))$ and give the boson-fermion realization with…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
We propose a conjectural correspondence between the spectra of the Bethe algebra for the quantum toroidal $\mathfrak{gl}_2$ algebra on relaxed Verma modules, and $q$-hypergeometric opers with apparent singularities. We introduce alongside…
For the case of quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ with $l = 1, 2$ we find the $\ell$-weights and the corresponding $\ell$-weight vectors for the representations obtained via Jimbo's homomorphism, known…
We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic…
A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…
We reconstruct the quantum enveloping superalgebra ${\bf U}(\mathfrak{gl}_{m|n})$ over $\mathbb Q(v)$ via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators of ${\bf…