Related papers: Categorification of based modules over the complex…

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…

We study the finite basis problem for $4$-element additively idempotent semirings whose additive reducts are quasi-antichains. Up to isomorphism, there are $93$ such algebras. We show that with the exception of the semiring $S_{(4, 435)}$,…

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…

We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given…

We show that the rings of invariants for the three dimensional modular representations of an elementary abelian $p$-group of rank four are complete intersections with embedding dimension at most five. Our results confirm the conjectures of…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

We introduce the notion of (nondegenerate) strong-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group SL(2,Z) whose kernel contains a…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

In this paper, we classify all irreducible weight modules with finite-dimensional weight spaces over the affine-Virasoro Lie algebra of type $A_1$.

We study projective presentations of finite-dimensional modules over finite-dimensional algebras. We discuss if projective presentations of maximal rank behave additively. More precisely, we ask if the direct sum of copies of a projective…

We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As…

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…

Let X be a complex projective curve which is smooth and irreducible of genus 2. The moduli space M_2 of semistable symplectic vector bundles of rank 4 over X is a variety of dimension 10. After assembling some results on vector bundles of…

Given a Lie superalgebra $\frak g$ with a subalgebra $\frak g_{\geq 0}$, and a finite-dimensional irreducible $\frak g_{\geq 0}$-module $F$, the induced $\frak g$-module $M(F)=U({\frak g}) \otimes_{U(\frak g_{\geq 0})} F $ is called a…

We study a particular category ${\cal{C}}$ of $\gl_{\infty}$-modules and a subcategory ${\cal{C}}_{int}$ of integrable $\gl_{\infty}$-modules. As the main results, we classify the irreducible modules in these two categories and we show that…

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…

In this paper we study the subcategory of cuspidal modules of the category of weight modules over the Lie algebra sl(n+1). Our main result is a complete classification and explicit description of the indecomposable cuspidal modules.

We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…

We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and…