noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...

A hypersurface D in C n is a linear free divisor if the module of logarithmic vector fields along D has a basis of global linear vector fields. It is then defined by a homogeneous polynomial of degree n and its complement is an open orbit of an algebraic subgroup G D of Gln(C) whose Lie algebra g D can be identified with that of linear logarithmic vector fields along D. We classify all linear f...

We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-computable and representation-directed coalgebras are characterized. The Auslander-Reiten quiver of a serial coalgebra is described. Finally, a version of Eisenbud-Griffith theorem is proved, namely, every subcoalgebra of a prime, hereditary and strictly quasi-finite coalgebra is serial. Introduction A syste...

We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)×U(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor struct...

This is an expository article on the singularities of nilpotent orbit closures in simple Lie algebras over the complex numbers. It is slanted towards aspects that are relevant for representation theory, including Ma ei's theorem relating Slodowy slices to Nakajima quiver varieties in type A. There is one new observation: the results of Juteau and Mautner, combined with Ma ei's theorem, give a g...

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflect...

Let G be an algebraic torus acting on a smooth variety V . We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V . Let G be a reductive algebraic group acting on a smooth variety V . The cotangent bundle T V admits a canonical algebraic symplectic structure, and the induced action of G on T V is hamiltonian, that is, it admits ...

Video-on-demand (VOD) servers need to be eeciently designed in order to support a large number of users viewing the same or diierent videos at diierent rates. In this paper, we propose the Quasi-static Interactive Video Retrieval (QuIVeR) Protocol for this purpose when disk-array based video servers are used. Five variations-QuIVeR-1, QuIVeR-2, QuIVeR-3, QuIVeR-4 and QuIVeR-5-are presented. The...