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...

We describe the design, implementation and user evaluation of QUIVER, a graph-based visual query language for object databases. The design goals of QUIVER include compliance to standards, comprehensive representational power, and consistency of visual representation. Compliance to standards is achieved through QUIVER queries being translated to OQL, the standard query language proposed by the O...

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...

We use free boson techniques to investigate AD -E-quiver matrix models. Certain higher spin fields in the free boson formulation give rise to higher order loop equations valid at finite N. These fields form a special kind of W-algebra, called Casimir algebra. We compute explicitly the loop equations for A r and D r quiver models and check that at large N they are related to a deformation of the...

Framed quiver moduli parametrize stable pairs consisting of a quiver representation and a map to a fixed graded vector space. Geometric properties and explicit realizations of framed quiver moduli for quivers without oriented cycles are derived, with emphasis on their cohomology. Their use for quantum group constructions is discussed.

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected quiver is Dynkin or extended Dynkin if and only if all moduli spaces of its representations are smooth.

We define a graph-based visual query language for object databases, called QUIVER. Most graph-based query languages proposed in the literature view queries either as constraint (pattern) graphs or as data-flow graphs. QUIVER, however, allows constraints and data-flow to be combined in queries. This combination of constraints and data-flow is motivated by the need to support comprehensive object...

Using subvarieties, which we call Demazure quiver varieties, of the quiver varieties of Nakajima, we give a geometric realization of Demazure modules of Kac-Moody algebras with symmetric Cartan data. We give a natural geometric characterization of the extremal weights of a representation and show that Lusztig's semicanonical basis is compatible with the filtration of a representation by Demazur...

For a perfect field k, we study actions of the absolute Galois group of k on the k-valued points of moduli spaces of quiver representations over k; the fixed locus is the set of k-rational points and we obtain a decomposition of this fixed locus indexed by elements in the Brauer group of k. We provide a modular interpretation of this decomposition using quiver representations over division alge...

We provide a common generalization of the Springer map and quiver-graded Springer map due to Lusztig, called generalized quiver-graded Springer map associated to generalized quiver representations introduced by Derksen and Weyman. Following Chriss and Ginzburg for any equivariant projective map π : E → V , there is an algebra structure on the equivariant Borel-Moore homology of Z = E ×V E, we c...