Counting representations of quivers over finite fields

Abstract

By counting the numbers of isomorphism classes of representations (indecomposable or absolutely indecomposable) of quivers over finite fields with fixed dimension vectors, we obtain a multi-variable formal identity. If the quiver has no edge-loops, this identity turns out to be a q-analogue of the Kac denominator identity modulus a conjecture of Kac. © 2000 Academic Press.