For any triple $(i,a,\mu)$ consisting of a vertex $i$ in quiver $Q$, positive integer $a$, and dominant $GL_a$-weight $\mu$, we define current $H^{(i,a)}_\mu$ acting on the tensor power $\Lambda^Q$ symmetric functions over vertices $Q$. These provide generalization parabolic Garsia-Jing creation operators theory Hall-Littlewood functions. $(\mathbf{i},\mathbf{a},\mu(\bullet))$ sequences such da...

We develop the theory of special biserial and string coalgebras and other concepts from the representation theory of quivers. These theoretical tools are then used to describe the finite dimensional comodules and Auslander-Reiten quiver for the coordinate Hopf algebra of quantum SL(2) at a root of unity. We also describe the stable Green ring. Let C = k ζ [SL(2)] denote the quantized coordinate...

We argue that there is an equivalence of M-theory on T 3 ×AN−1 with a fourdimensional non-supersymmetric quiver gauge theory on the Higgs branch. The quiver theory in question has gauge group SU(N)N4N6N8 and is considered in a strong coupling and large N4,6,8 limit. We provide fieldand string-theoretical evidence for the equivalence making use of the deconstruction technique. In particular, we ...

Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti–Córdova–Vafa in the context of supersymmetric gauge theory. The existence of maximal green sequences for exceptional finite mutation type quivers has been shown by Alim–Cecotti–Córdova–Espahbodi–Rastogi–Vafa except...

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natura...

We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman’s complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex resolves a maximal Cohen-Macaulay module supported on the quiver determinantal variety. This allows us to find the set-theoretical defining equat...

N = 2 quiver Chern-Simons theory has lately attracted attention as the world volume theory of multiple M2 branes on a Calabi-Yau 4-fold. We study the connection between the stringy derivation of M2 brane theories and the forward algorithm which gives the toric Calabi-Yau 4-fold as the moduli space of the quiver theory. Then the existence of the 3+1 dimensional parent, which is the consistent 3+...

This paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver. To accomplish this, we study the quiver Q with relations R corresponding to the finite-dimensional algebra End ( ⊕r i=0 Li) where L := (OX , L1, . . . , Lr) is a list of line bundles on a projective toric variety X. The quiver Q defines a smooth projective to...

Let A and B be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence α between A and B such that α is induced by exact functors. We present a nice correspondence between indecomposable modules over A and B. As a consequence, we have the following: (1) If A is a self-injective algebra, then so is B; (2) If A and B are finite dimensional algebras over an algeb...

We determine the minimal lower bound n, with $$n \geqslant 1$$ , where n-th power of radical module category a representation-finite cluster tilted algebra vanishes. give such in terms number vertices underline quiver. Consequently, we get nilpotency index for self-injective algebras. also study non-zero composition m, $$m 2$$ irreducible morphisms between indecomposable modules algebras lying ...