Related papers: Categorification of based modules over the complex…
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…
Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\hat{A}(m,n)$ ($m\ne n$) or $\hat{C}(m)$. Here we treat the latter affine superalgebras…
In this survey, we shall be concerned with the category of finite-dimensional representations of the untwisted quantum affine algebras when the quantum parameter q is not a root of unity. We review the foundational results of the subject,…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
It is proved that an irreducible quasifinite $W_\infty$-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight $W_\infty$-module is a module of the intermediate series.…
In this paper we classify all simple weight modules for a quantum group $U_q$ at a complex root of unity $q$ when the Lie algebra is not of type $G_2$. By a weight module we mean a finitely generated $U_q$-module which has finite…
We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a presentation of a module to an $R$-diagram. The latter is the…
This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main…
We classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring R by using integer-valued functions on Spec R. As an application we give a complete classification of resolving subcategories when…
Contravariantly finite resolving subcategories of the category of finitely generated modules have been playing an important role in the representation theory of algebras. In this paper we study contravariantly finite resolving subcategories…
In this paper, Lie conformal superalgebras of rank (2 + 1) are completely classified (up to isomorphism) and their automorphism groups are determined. Furthermore, we give the classification of the finite irreducible conformal modules over…
In this paper it is proved that an irreducible weight module with finite-dimensional weight spaces over the Schr\"{o}dinger-Virasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable…
In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…
In [20] Esnault asked whether on a general quotient surface singularity the rank and the first Chern class distinguish isomorphism classes of indecomposable reflexive modules. Wunram gave a contraexample in [46] showing two different full…
The aim of this note is to understand under which conditions invertible modules over a commutative S-algebra in the sense of Elmendorf, Kriz, Mandell and May give rise to elements in the algebraic Picard group of invertible graded modules…
We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…
The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated…
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…
We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that…
We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules…