Related papers: A Combinatorial Study on Quiver Varieties

EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

In the case of Dynkin quivers we establish a formula for the Grothendieck class of a quiver cycle as the iterated residue of a certain rational function, for which we provide an explicit combinatorial construction. Moreover, we utilize a…

We investigate a family of representations of Gale-Robinson quivers that are geared towards providing concrete information about the corresponding cluster algebras. In this way, we provide a representation theoretic explanation for known…

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…

This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…

We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some…

The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial…

In this short note we prove a couple of facts about polynomial count varieties, answering natural questions that they raise. A polynomial count $X$ variety is essentially one for which its number of points over finite fields is given by a…

We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable…

This paper deals with the representation theory of a locally finite quiver in which the number of paths between any two given vertices is finite. We first study some properties of the finitely presented or co-presented representations, and…

We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type C. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we…

We construct Nakajima's quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy's) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into…

For an arbitrary quiver Q and dimension vector d we prove that the dimension of the space of cuspidal functions on the moduli stack of representations of Q of dimension d over a finite field F_q is given by a polynomial in q with rational…

For an arbitrary equidimensional quiver representation, we proposed the method of construction of a system of free generators of the field of $U$-invariants. The construction of the section and system of generators depends on the choice of…

We present a conjecture generalizing the Cauchy formula for Macdonald polynomials. This conjecture encodes the mixed Hodge polynomials of the character varieties of representations of the fundamental group of a Riemann surface of genus g to…

Exceptional sequences are important sequences of quiver representations in the study of representation theory of algebras. They are also closely related to the theory of cluster algebras and the combinatorics of Coxeter groups. We…

We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with…

We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we give an explicit weight- and length-preserving bijection…