Related papers: On characters of $L_{\frak{sl}_n}(-\Lambda_0)$-mod…

In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…

We study the level-one irreducible highest weight representations of $U_q[\hat{gl(1|1)}]$ and associated q-vertex operators. We obtain the exchange relations satisfied by the vertex operators. The characters and supercharacters associated…

The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In…

In this paper, we study a class of $\Z_d$-graded modules, which are constructed using Larsson's functor from $\sl_d$-modules $V$, for the Lie algebras of divergence zero vector fields on tori and quantum tori. We determine the…

The goals of this article are as follows: (1) To determine the irreducible components of the affine varieties parametrizing the representations of $ \Lambda $ with dimension vector d, where $ \Lambda $ traces a major class of finite…

For a root system R, a field K and an invertible element q in K let U be the associated quantum group, defined via Lusztig's divided powers construction. We study the irreducible characters of this algebra with integral (but not necessarily…

We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$ having rank $l$ and let $V=L(\lambda)$ be an irreducible finite-dimensional $\mathfrak{g}$-module having highest weight $\lambda.$ Computations of weight multiplicities in…

We construct irreducible representations of affine Khovanov-Lauda-Rouquier algebras of arbitrary finite type. The irreducible representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that…

We prove a closed character formula for the symmetric powers $S^N V(\lambda)$ of a fixed irreducible representation $V(\lambda)$ of a complex semi-simple Lie algebra $\mathfrak{g}$ by means of partial fraction decomposition. The formula…

Affine Lie algebras admit non-classical highest-weight theories through alternative partitions of the root system. Although significant inroads have been made, much of the classical machinery is inapplicable in this broader context, and…

Let $G$ be a connected reductive group over the complex numbers and let $T\subset G$ be a maximal torus. For any $t\in T$ of finite order and any irreducible representation $V(\lambda)$ of $G$ of highest weight $\lambda$, we determine the…

The modular properties of characters of representations of a family of W-superalgebras extending the affine Lie superalgebra of gl(1|1) are considered. Modules fall into two classes, the generic type and the non-generic one. Characters of…

The aim of this paper is to study the canonical filtration $L(\lambda)_l$ of an irreducible finite dimensional $\operatorname{SL}(V)$-module $L(\lambda)$ using the universal enveloping algebra $U(\mathfrak{sl}(V))$ and the annihilator ideal…

We give a combinatorial formula for the character of a finite-dimensional irreducible representation of the periplectic Lie superalgebra $\mathfrak{p}(n)$. The character of irreducible module $L(\mu)$ is given by a cancellation-free…

In this note we determine when is an induced module H^0_G(\lambda), corresponding to a dominant integral highest weight \lambda of the general linear supergroup G=GL(m|n) irreducible. Using the contravariant duality given by the supertrace…

In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(\lambda),L_n(\mu))$, where GL(n) is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(\lambda)$ and $L_n(\mu)$ are rational…

A level-one representation of the quantum affine superalgebra $\U_q(\hat{\frak{sl}}(M+1|N+1))$ and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields. Character formulas of…

The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak q(n)$ over $\C$ was solved in 1996 by I. Penkov and V. Serganova. In this article, we give a different approach…