Related papers: Representations of reflection algebras

In \cite{GS1} the notion of braided Yangians of Reflection Equation type was introduced. Each of these algebras is associated with an involutive or Hecke symmetry $R$. Besides, the quantum analogs of certain symmetric polynomials…

We give explicit actions of Drinfeld generators on Gelfand-Tsetlin bases of super Yangian modules associated with skew Young diagrams. In particular, we give another proof that these representations are irreducible. We study irreducible…

We discuss highest $\ell$-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and $q$-oscillator representations of the…

We study representations of the central extension of the Lie algebra of differential operators on the circle, the W-infinity algebra. We obtain complete and specialized character formulas for a large class of representations, which we call…

Representation theory of an infinite dimensional Galilean conformal algebra introduced by Martelli and Tachikawa is developed. We focus on the algebra defined in (2+1) dimensional spacetime and consider central extension. It is then shown…

We define a class of quantum linear Galois algebras which include the universal enveloping algebra Uq(gln), the quantum Heisenberg Lie algebra and other quantum orthogonal Gelfand-Zetlin algebras of type A, the subalgebras of G-invariants…

We determine the intertwiners of a family of Onsager coideal subalgebras of the quantum affine algebra $U_p(A^{(1)}_{n-1})$ in the fundamental representations and $U_p(B^{(1)}_{n}), U_p(D^{(1)}_{n}), U_p(D^{(2)}_{n+1})$ in the spin…

The periplectic Lie superalgebra $\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in…

Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…

In this article a complete description is given of the simple representations of a 3-dimensional Sklyanin algebra associated to a torsion point. In order to determine these irreducible representations, a review is given of classical results…

We show that the Yangian Yn over gl_n possesses some features of the ring of regular functions on GL_n. In particular, we use the theory of quasideterminants to construct noncommutative flags associated to Yn. In so doing, a class of…

Let Uq(g) be the quantum affine superalgebra associated with an affine Kac-Moody superalgebra g which belongs to the three series osp(1|2n)^(1),sl(1|2n)^(2) and osp(2|2n)^(2). We develop vertex operator constructions for the level 1…

We construct a wide class of finite W-algebras as truncations of Yangians. These truncations correspond to algebra homomorphisms and allow to construct the W-algebras as exchange algebras, the R-matrix being the Yangian's one. As an…

We classify right coideal subalgebras of the finite-dimensional quotient of the quantized enveloping algebra $U_q(\mathfrak{sl}_2)$ and that of the quantized coordinate algebra $\mathcal{O}_q(SL_2)$ at a root of unity $q$ of odd order. All…

In this paper we study a relationship between systems of $n$ subspaces and representations of $*$-algebras generated by projections. We prove that irreducible nonequivalent $*$-representations of $*$-algebras $\mathcal P_{4,com}$ generate…

Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic…

We propose the study and description of the structure of complex Lie algebras with nilradical a nilpotent Lie algebra of type 2 by using sl2(C)-representation theory. Our results will be applied to review the classification given in [1] (J.…

Olshanski's centralizer construction provides a realization of the Yangian for the Lie algebra gl(n) as a subalgebra in the projective limit of a chain of centralizers in the universal enveloping algebras. We give a modified version of this…

We consider the finite Weyl groups of classical type -- $W(A_{r})$ for $r \geq 1$, $W(B_{r}) = W(C_{r})$ for $r \geq 2$, and $W(D_{r})$ for $r \geq 4$ -- as supergroups in which the reflections are of odd superdegree. Viewing the…

Let $\mathfrak g$ be a reductive Lie algebra, and $m$ a positive integer. There is a natural density of irreducible representations of $\mathfrak g$, whose degrees are not divisible by $m$. For $\mathfrak g=\mathfrak{gl}_n$, this density…