Related papers: Representations of Quantum Affine Superalgebras

This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(\mathfrak{g})$, Yangian $Y(\mathfrak{g})$ and…

We consider the quantum symmetric pair $(\mathcal{U}_q(\mathfrak{su}(3)), \mathcal{B})$ where $\mathcal{B}$ is a right coideal subalgebra. We prove that all finite-dimensional irreducible representations of $\mathcal{B}$ are weight…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

We study the category of finite--dimensional representations for a basic classical Lie superalgebra $\Lg=\Lg_0\oplus \Lg_1$. For the ortho--symplectic Lie superalgebra $\Lg=\mathfrak{osp}(1,2n)$ we show that certain objects in that category…

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…

In the first part of the paper we give the denominator identity for all simple finite-dimensional Lie super algebras $\frak g\/$ with a non-degenerate invariant bilinear form. We give also a character and (super) dimension formulas for all…

The Brylinski-Kostant filtration on a representation of a finite-dimensional semisimple Lie algebra has interpretations in terms of the algebra, geometry and combinatorics of the representation. Its extension to affine Lie algebras was…

We study a class of algebras B(n,l) associated with integrable models with boundaries. These algebras can be identified with coideal subalgebras in the Yangian for gl(n). We construct an analog of the quantum determinant and show that its…

Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be…

We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are…

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…

Given any pair of positive integers m and n, we construct a new Hopf algebra, which may be regarded as a degenerate version of the quantum group of gl(m+n). We study its structure and develop a highest weight representation theory. The…

We define the categories of weight-finite modules over the type $\mathfrak a_1$ quantum affine algebra $\dot{\mathrm{U}}_q(\mathfrak a_1)$ and over the type $\mathfrak a_1$ double quantum affine algebra $\ddot{\mathrm{U}}_q(\mathfrak a_1)$…

We give a detailed derivation of the commutation relations for the Poincar\'e--Birkhoff--Witt generators of the quantum superalgebra $\mathrm U_q(\mathfrak{gl}_{M|N})$.

In this paper we extend general results obtained by V. Kac and J. Liberati, in "Unitary quasifinite representations of $W_\infty$", (Letters Math. Phys., 53 (2000), 11-27), for quasifinite highest weight representations of $\Z$-graded Lie…

We consider two algebraic invariants in the representation theory of quantized enveloping algebras: the dimension growth of simple modules for the De Concini-Kac quantum group at roots of unity, and the Gelfand-Kirillov dimension of simple…

We introduce and study a category $\text{Fin}$ of modules of the Borel subalgebra of a quantum affine algebra $U_q\mathfrak{g}$, where the commutative algebra of Drinfeld generators $h_{i,r}$, corresponding to Cartan currents, has finitely…

We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of $W$ infinity algebras ($W_{\infty}$, $W_{1+\infty}$, $W_{\infty}^{1,1}$, $W_{\infty}^M$, $W_{1+\infty}^N$,…

We give a precise expression for the universal weight function of the quantum affine algebra $U_q(\hat{sl}_3)$. The calculations use the technique of projecting products of Drinfeld currents on the intersections of Borel subalgebras.

We define for real $q$ a unital $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ quantizing the universal enveloping $*$-algebra of $\mathfrak{sl}(2,\mathbb{R})$. The $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ is realized as a…