Related papers: Representation theory of type B and C standard Lev…

We introduce a new way to study representations of the Lie superalgebra $p(n)$. Since the center of the universal enveloping algebra $U$ acts trivially on all irreducible representations, we suggest to study the quotient algebra $\bar{U}$…

We give a graded dimension formula described in terms of combinatorics of Young diagrams and a simple criterion to determine the representation type for the finite quiver Hecke algebras of type $C_{\ell}^{(1)}$.

Locally affine Lie algebras are generalizations of affine Kac--Moody algebras with Cartan subalgebras of infinite rank whose root system is locally affine. In this note we study a class of representations of locally affine algebras…

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

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…

Let G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classified. We describe a simple algorithm for finding a…

For every finite dimensional Lie supergroup $(G,\mathfrak g)$, we define a $C^*$-algebra $\mathcal A:=\mathcal A(G,\mathfrak g)$, and show that there exists a canonical bijective correspondence between unitary representations of…

Let $L_c$ be simple vertex operator superalgebra(SVOA) associated to the vacuum representation of N=2 superconformal algebra with the central charge $c$. Let $c_m = {3m}/{m+2}$. We classify all irreducible modules for the SVOA $L_{c_m}$.…

Using the skew-symmetry of the differential operators and multiplication operators in the canonical representations of finite-dimensional classical Lie algebras, we obtain some noncanonical polynomial representations of the classical Lie…

For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the…

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…

Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…

We construct irreducible modules V_{\alpha}, \alpha \in \C over W_3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights of modules…

We classify all irreducible highest-weight unitary modules over the non-compact real form $\mathfrak{u}(p,q|n)$ of the general linear Lie superalgebra $\mathfrak{gl}_{p+q|n}$. The classification is given by explicit necessary and sufficient…

In a recent paper, V. Dobrev and A. Sudbery classified the highest-weight and lowest-weight finite dimensional irreducible representations of the quantum Lie algebra sl(2)_q introduced by V. Lyubashenko and A. Sudbery. The aim of this note…

In this paper, we study representations of non-finitely graded Lie algebras $\mathcal{W}(\epsilon)$ related to Virasoro algebra, where $\epsilon = \pm 1$. Precisely speaking, we completely classify the free $\mathcal{U}(\mathfrak…

An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having…

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…

We give a complete description of the bounded (i.e. norm continuous) unitary representations of the Fr\'echet-Lie algebra of all smooth sections, as well as of the LF-Lie algebra of compactly supported smooth sections, of a smooth Lie…