Abstract
AbstractLet Q be a quiver of type
$\tilde {A}_n$
. Let
$\alpha =\alpha _1+\alpha _2+\cdots +\alpha _s$
be the canonical decomposition. For the polynomials
$M_Q(\alpha ,q)$
that count the number of isoclasses of representations of Q over
${\mathbb F}_q$
with dimension vector
$\alpha $
, we obtain a precise relation between the degree of
$M_Q(\alpha ,q)$
and that of
$\prod _{i=1}^{s} M_Q(\alpha _i,q)$
for an arbitrary dimension vector
$\alpha $
.
Publisher
Cambridge University Press (CUP)