Semisimple representations of quivers in characteristic p
by
M. Domokos
Rényi Institute, Budapest, Hungary
Coauthors: A. N. Zubkov (Omsk, Russia)

We study representations of quivers over an algebraically closed base field k. There is an affine variety V(Q, d) parameterizing semisimple representations of the quiver Q with dimension vector d, constructed by polynomial invariants. When k is of characteristic zero, interpreting Luna's theory of étale slices in terms of representation theory Le Bruyn and Procesi obtained a finite stratification of V(Q, d) into smooth, irreducible, locally closed subvarieties. They showed that the study of the étale local structure of V(Q, d) can often be reduced to another quiver setting.

Using theorems of Bardsley-Richardson and Donkin we show that the above results hold also in characteristic p. In particular, the description of the simple dimension vectors given by Le Bruyn and Procesi remains valid in any characteristic.

Date received: June 23, 2000