Related papers: Tree normal forms for quiver representations

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

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…

When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…

Let k be a field and A the n-Kronecker algebra, this is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is well-known that the dimension vectors of the indecomposable…

We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of…

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…

We use the theory of differential tensor algebras and their modules to produce explicit representations of extended Dynkin quivers.

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae that take symmetries into account as a starting point.…

Generalizing Schubert cells in type A and a cell decomposition if Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of an oriented cycle admit an affine cell decomposition…

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…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

The space of elliptic modular forms of fixed weight and level can be identfied with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying…

We construct the irreducible unipotent modules of the finite general linear groups using tableaux. Our construction is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction…

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…

We provide a general construction procedure for antilinearly invariant complex root spaces. The proposed method is generic and may be applied to any Weyl group allowing to take any element of the group as a starting point for the…

We construct large families of simple modules for untwisted affine Lie algebras using induction from one-dimensional modules over nilpotent loop subalgebras. We also show that the vector space of the first self-extensions for these module…

Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…

In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class…

We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…