We study preprojective algebras of graphs and their relationship to module categories over
representations of quantum SL (2). As an application, ADE quiver varieties of Nakajima are …

arXiv:math/0302130v1 [math.QA] 11 Feb 2003 Page 1 arXiv:math/0302130v1 [math.QA] 11
Feb 2003 MODULE CATEGORIES OVER REPRESENTATIONS OF SLq(2) AND GRAPHS …

A monoid structure on families of representations of a quiver is introduced by taking
extensions of representations in families, that is, subvarieties of the varieties of …

Quivers play an important role in the representation theory of algebras, with a key ingredient
being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of …

1. Introduction. This paper is a sequel of [27]. In the previous paper, we defined a new family
of hyper-K/ihlermanifolds, called quiver varieties, associated to finite graphs without edge …

We give a crystal structure on the set of all irreducible components of Lagrangian
subvarieties of quiver varieties. One can show that, as a crystal, it is isomorphic to the crystal …

Mathematical Physics A Quiver Quantum Group Page 1 Commun. Math. Phys. 157, 459-177
(1993) Communications IΠ Mathematical Physics © Springer-Verlag 1993 A Quiver Quantum …

We categorify the highest weight integrable representations and their tensor products of a
symmetric quantum Kac-Moody algebra. As a byproduct, we obtain a geometric realization …

Inspired by recent work of Hernandez–Leclerc and Leclerc–Plamondon we investigate the
link between Nakajima's graded affine quiver varieties associated with an acyclic connected …

0.1. Let us consider a finite graph in which no edge joins a vertex with itself. This graph
defines a symmetric matrix (ai1) indexed by pairs of vertices of the graph, where aii= 2 and …