Related papers: Finite Dimensional Representations of the Projecti…

We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…

To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…

A self-contained introduction to infinite dimensional representations over a tame hereditary algebra is provided, assuming a basic knowledge of the category of finite dimensional representations. This includes a complete description of all…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…

For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{rep}(Q)$ of pointwise finite dimensional representations. We show that an object in…

Let $X$ and $\mathfrak{a}$ be an affine scheme and (respectively) a finite-dimensional associative algebra over an algebraically-closed field $\Bbbk$, both equipped with actions by a linearly-reductive linear algebraic group $G$. We…

The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.

Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional formulas, Dynkin indices, quadratic Casimir…

This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(\mathfrak{g})$, Yangian $Y(\mathfrak{g})$ and…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

We investigate the categories of finite-dimensional representations of multicurrent and multiloop hyperalgebras in positive characteristic, i.e., the hyperalgebras associated to the multicurrent algebras $\mathfrak…

Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…

Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…