Related papers: Categorifications of Non-Integer Quivers: Type $I_…

An alternative "flipped" version of the quartification model is obtained by rearrangement of the particle assignments. The model has two standard (trinification) families and one flipped quartification family. An interesting…

In previous work, Takagi used the methods of solving the Sarkisov links by calculating the corresponding Diophantine equations and the construction of key varieties to give all possible classifications and some implementations of a class…

We give a classification of infinite dimensional indecomposable weight modules over the Lie superalgebra $sl(2/1)$.

We calculate quark Wigner distributions using the light-front wave functions in a dressed quark model. In this model, a proton target is replaced by a simplified spin-1/2 state, namely a quark dressed with a gluon. We calculate the Wigner…

Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed…

We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex…

We introduce two new sets of invariant functions of quark mass matrices, which express the constraints on these mass matrices due to knowledge of the quark mixing matrix. These invariants provide a very simple method to test candidate forms…

We provide a categorification of Oh and Suh's combinatorial Auslander-Reiten quivers in the simply laced case. We work within the perfectly valued derived category $\mathrm{pvd}(\Pi_Q)$ of the 2-dimensional Ginzburg dg algebra of a Dynkin…

We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.

We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on surfaces, modular forms and multiplicities in…

We compute the quiver of any monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term…

The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work) to classify exceptional sequences of representations of Q,…

This note informally describes a way to build certain cubical n-categories by iterating a process of taking models of certain finite limits theories. We base this discussion on a construction of "double bicategories" as bicategories…

Let us consider a specialization of an untwisted quantum affine algebra of type $ADE$ at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases,…

We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is…

We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper…

For a finite dimensional hereditary algebra, we consider: exceptional sequences in the category of finite dimensional modules, silting objects in the bounded derived category, and m-cluster tilting objects in the m-cluster category. There…

We study the representation category of thread quivers and their quotients. A thread quiver is a quiver in which some arrows have been replaced by totally ordered sets. Pointwise finite-dimensional (pwf) representations of such a thread…