相关论文: Cartan-Weyl basis for Quantum Affine Superalgebra …
We shall give some criteria for the existence of the Peter-Weyl type decomposition for modified quantum algebra, which is motivated by the fact that modified quantum algebra has commutative two crystal structures. We shall apply the…
The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter - Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum…
We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q =…
Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the…
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…
We study a deformed $su(m|n)$ algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed…
An algebraic structure, Quotient Algebra Partition or QAP, is introduced in a serial of articles. The structure QAP is universal to Lie Algebras and enables algorithmic and exhaustive Cartan decompositions. The first episode draws the…
In this paper, we develop the crystal basis theory for the quantum queer superalgebra $\Uq$. We define the notion of crystal bases, describe the tensor product rule, and present the existence and uniqueness of crystal bases for…
Using the corepresentation of the quantum supergroup OSp_q(1/2) a general method for constructing noncommutative spaces covariant under its coaction is developed. In particular, a one-parameter family of covariant algebras, which may be…
We give the explicit formula of the universal $R$-matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type ${\mathrm{A}}_1^{(1)}$. For $N$ with $q_{00}q_{01}$ being a primitive $N$-th root of unity,…
This is the sequel exposition following [1]. The framework quotient algebra partition is rephrased in the language of the s-representation. Thanks to this language, a quotient algebra partition of the simplest form is established under a…
We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras…
The Racah problem for the quantum superalgebra $\mathfrak{osp}_{q}(1|2)$ is considered. The intermediate Casimir operators are shown to realize a $q$-deformation of the Bannai-Ito algebra. The Racah coefficients of $\mathfrak{osp}_q(1|2)$…
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…
Fusion coefficients for affine Lie algebras are fixed by the corresponding tensor-product coefficients and a set of threshold levels. It is shown how the information concerning the threshold level is coded in the fusion basis, which is a…
We consider principal subspace W({\Lambda}) of integrable highest weight module L({\Lambda}) for quantum affine algebra $U_q(\hat{\mathfrak{sl}}_{n+1})$. We introduce quantum analogues of the quasi-particles associated with the principal…
Generalizing our earlier work, we introduce the homogeneous quantum $Z$-algebras for all quantum affine algebras $\alg$ of type one. With the new algebras we unite previously scattered realizations of quantum affine algebras in various…
Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by…
A boson representation of the quantum affine algebra $U_q(\widehat{\sl}_2)$ is realized based on the Wakimoto construction. We discuss relations with the other boson representations.
We describe the twisted affine superalgebra $sl(2|2)^{(2)}$ and its quantized version $U_q[sl(2|2)^{(2)}]$. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra…