We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an ADE quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with ADE global symmetry. This equivalence suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theor...

Let → Γ be a valued quiver. Let C be the symmetrizable generalized Cartan matrix associated to → Γ. We show that the whole quantum group associated to C can be realized from the category of the representations of the product valued quiver → Γ. This method can be used to realize the whole generalized Kac-Moody Lie algebra associated to C, as discussed in [LL].

For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. MSC(2000): 16E40, 16E10, 16G10

We derive a combinatorial formula for quantized Donaldson-Thomas invariants of the m-loop quiver. Our main tools are the combinatorics of noncommutative Hilbert schemes and a degenerate version of the Cohomological Hall algebra of this quiver. 2010 Mathematics Subject Classification: Primary 16G20, secondary 05E05, 14N35

This work connects the idea of a “blow-up” of a quiver with that of injectivity, showing that for a class of monic maps Φ, a quiver is Φ-injective if and only if all blow-ups of it are as well. This relationship is then used to characterize all quivers that are injective with respect to the natural embedding of Pn into Cn.

We investigate boundary states of N = 2 coset models based on Grassmannians Gr(n, n+k), and find that the underlying intersection geometry is given by the fusion ring of U (n). This is isomorphic to the quantum cohomology ring of Gr(n, n+k+1), which in turn can be encoded in a " boundary " superpotential whose critical points correspond to the boundary states. In this way the intersection prope...

We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras Rn of type A when e = 0 (the linear quiver) or e ≥ n. We show that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When e = 0 we show that the KLR grading on the quiver Hecke algebras is compatible with the gradings on parabolic category OΛ n previous...

Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of endowed with a bracket. In this work, we provide study morphisms double algebras, which relate to the $H_0$-Poisson structures Crawley-Boevey. We prove in particular that algebra structure defined for an arbitrary quiver only depends upon seen undirected graph, up isomorphism. derive from our result...

This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type A. The quiver flag variety Mθ(Q, r) of a finite acyclic quiver Q (with a unique source) and a dimension vector r is a fine moduli space of stable representations of Q. Quiver flag varieties are Mori Dream Spaces, they are obtained via a tower of Grassmann bu...