Some remarks on Nakajima's quiver varieties of type A
We try to clarify the relations between quiver varieties of type A and Kraft-Pocesi proof of normality of nilpotent conjugacy classes closures.
math.RT↗
arXiv subjects
D. A. Shmelkin
Publications and source records attributed to D. A. Shmelkin.
Some algorithms for semi-invariants of quivers
We present some theorems and algorithms for calculating perpendicular categories and locally semi-simple decompositions. We implemented a computer program {\sc TETIVA} based on these algorithms and we offer this program for everybody's use.
math.RT↗
Locally semi-simple representations of quivers
We suggest a geometrical approach to the semi-invariants of quivers based on Luna's slice theorem and the Luna-Richardson theorem. The locally semi-simple representations are defined in this spirit but turn out to be connected with stable representations in the sense of GIT, Schofield's perpendicular categories, and Ringel's regular representations. As an application of this method we obtain an independent short proof of the theorem of Skowronsky and Weyman about semi-invariants of the tame quivers.
math.AG↗
Signed quivers, symmetric quivers, and root systems
We define a special sort of weighted oriented graphs, signed quivers. Each of these yields a symmetric quiver, i.e., a quiver endowed with an involutive anti-automorphism and the inherited signs. We develop a representation theory of symmetric quivers, in particular we describe the indecomposable symmetric representations. Their dimensions constitute root systems corresponding to certain symmetrizable generalized Cartan matrices.
math.AG↗