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Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…
We investigate the representations of the exotic conformal Galilei algebra. This is done by explicitly constructing all singular vectors within the Verma modules, and then deducing irreducibility of the associated highest weight quotient…
An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…
We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the…
We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…
Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…
We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
In this paper we classified irreducible modules for the loop of derivations of rational quantum torus with associative $\mathbb{C}_q^1\otimes B$ action and anti-associative $\mathbb{C}_q^2\otimes B$ action on the modules.
We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…
This paper classifies irreducible, integrable highest weight modules for "current Kac-Moody Algebras" with finite dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many…
We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.
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 classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).
We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irreducible representations of dimension at most n for a simple…
We discuss irreducible highest weight representations of the sl(2) loop algebra and reducible indecomposable ones in association with the sl(2) loop algebra symmetry of the six-vertex model at roots of unity. We formulate an elementary…
The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…
We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.