Related papers: Picture groups and maximal green sequences

We characterize the ``best'' model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct ``best'' model geometries in an appropriate sense--these are the maximally symmetric trees. The…

We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…

We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

We show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse Coxeter element in the Weyl group. We use this result to give a new combinatorial…

We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an…

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations…

We associate a combinatorial object to sequences of point blow-ups over perfect fields, the weighted directed graph, and another one to the composition of all blow-ups, which we call associated sequential morphisms, the $d-$ary intersection…

We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These representations can be viewed as a natural generalization of the geometric representation. The…

There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer $D$, the set of Hilbert series of right-sided ideals with generators and relations of…

Colouring problems arising from group-based constructions provide a natural link between combinatorics and algebra, particularly in the study of Cayley graphs and Latin squares. We introduce the notion of colouring bijections of finite…

We conjecture the existence of special elements in odd degree higher algebraic K-groups of number fields that are related in a precise way to the values at strictly negative integers of the derivatives of Artin L-functions of finite…

We prove a version of Gabriel's theorem for (possibly infinite dimensional) representations of infinite quivers. More precisely, we show that the representation theory of quiver $\Omega$ is of unique type (each dimension vector has at most…

Let $X_r$ be a finite type Dynkin diagram, and $\ell$ be a positive integer greater than or equal to two. The $Y$-system of type $X_r$ with level $\ell$ is a system of algebraic relations, whose solutions have been proved to have…

The higher direct image complex of a coherent sheaf (or finite complex of coherent sheaves) under a projective morphism is a fundamental construction that can be defined via a Cech complex or an injective resolution, both inherently…

We introduce the notions of $\tau$-exceptional and signed $\tau$-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \leq n$, there is a bijection between…

We show that all totally positive formal power series with integer coefficients and constant term $1$ are precisely the rank-generating functions of Schur-positive upho posets, thereby resolving the main conjecture proposed by Gao, Guo,…

The Chen groups of a group $G$ are the lower central series quotients of the maximal metabelian quotient of $G$. Under certain conditions, we relate the ranks of the Chen groups to the first resonance variety of $G$, a jump locus for the…

In this paper authors consider representations of graphs in Hilbert spaces applying a restriction of local scalarity on them. It enables to obtain a theory, similar to the classical theory of representations of graphs in vector spaces. In…

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a…