Related papers: Weighted quivers

We describe the cohomology groups of a homogeneous vector bundle $E$ on any Hermitian symmetric variety $X=G/P$ of ADE type as the cohomology of a complex explicitly described. The main tool is the equivalence between the category of…

We show that a finite connected quiver Q with no oriented cycles is tame if and only if for each dimension vector $\mathbf{d}$ and each integral weight $\theta$ of Q, the moduli space $\mathcal{M}(Q,\mathbf{d})^{ss}_{\theta}$ of…

We construct the Chow weight structure on the derived category of geometric motives with arbitrary coefficients for X a finite type scheme over a field characteristic 0 and G an affine algebraic group. In particular we also show that the…

A codeword is associated to a linearized polynomial. The weight distribution of the codewords is determined as the linearized polynomial varies in a family of fixed degree. There is a corresponding result on Wenger graphs from linearized…

Quandle Coloring Quivers are directed graph-valued invariants of classical and virtual knots and links associated to finite quandles. Quandle action quivers are subquivers of the full quandle coloring quiver associated to quandle actions by…

A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the…

Let $G$ be a finite group acting on an ice quiver with potential $(Q, F, W)$. We construct the corresponding $G$-equivariant relative cluster category and $G$-equivariant Higgs category, extending the work of Demonet. Using the orbit…

We introduce a new series $R_k$, $k=2,3,4,\dots$, of integer valued weight systems. The value of the weight system $R_k$ on a chord diagram is a signed number of cycles of even length $2k$ in the intersection graph of the diagram. We show…

We introduce a new infinite family of enhancements of the biquandle homset invariant called biquandle arrow weights. These invariants assign weights in an abelian group to intersections of arrows in a Gauss diagram representing a classical…

Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…

Inspirited by the importance of the spectral theory of graphs, we introduce the spectral theory of valued cluster quiver of a cluster algebra. Our aim is to characterize a cluster algebra via its spectrum so as to use the spectral theory as…

Kervaire conjecture that the weight of the free product of every non-trivial group and the infinite cyclic group is not one is confirmed by confirming Conjecture Z of a knot exterior.

We propose a mutation formula for the general rank from a principal component ${\rm PC}(\delta)$ of representations to another one ${\rm PC}(\epsilon)$ for a quiver with potential. We give sufficient conditions for the formula to hold. In…

In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.

The (ordinary) quiver of an algebra $A$ is a graph that contains information about the algebra's representations. We give a description of the quiver of $\mathbb{C}PT_{n}$, the algebra of the monoid of all partial functions on $n$ elements.…

We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which…

We prove the basic properties of determinantal semi-invariants for presentation spaces over any finite dimensional hereditary algebra over any field. These include the virtual generic decomposition theorem, stability theorem and the…

Let G be a Lie group and Q a quiver with relations. In this paper, we define G-valued representations of Q which directly generalize G-valued representations of finitely generated groups. Although as G-spaces, the G-valued quiver…

Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In…

In this paper we introduce the notion of weighted (weakly) almost periodic compactifcation of a semitopological semigroup and generalize this notion to corresponding notion for transformation semigroup.The inclusion relation and equality of…