we consider the positive integers (cf. §\[algclose\] for more details)

$$d:={\rm dim}\,\{(x,g)\in\rep^\alpha(Q,\R)\times\G_\alpha(\R)\,|\,g\cdot x=x\}-{\rm dim}\, \G_\alpha(\R)$$ and the number $c$ of irreducible components of $\{(x,g)\in\rep^\alpha(Q,\R)\times\G_\alpha(\R)\,|\,g\cdot x=x\}$ of maximal dimension (here our $\R$-schemes are regarded as $\k$-schemes). The pair $(c,d)$ gives us thus an estimation of the size of the orbit space $\rep^\alpha(Q,\R)/\G_\alpha(\R)$. Note that if $d=0$, then the orbit space is finite of cardinality $c$. By abuse of notation we also use the notation $m_\alpha(\R Q)$ to denote the pair $(c,d)$ in the algebraically closed field case.

Given two representations of $Q$ over $\R$ we can form their direct sum. We define an [indecomposable]{} representation of $Q$ over $\R$ as one which is not isomorphic with a direct sum of two non-trivial representations. If we assume that $\R$ is local then the category of locally free representations is Krull-Schmidt. Therefore when talking about indecomposable representations we will always assume that $\R$ is a local Frobenius $\k$-algebra which we will further assume to be *split* (see §\[Frobsection\]). When $M$ is a representation of $Q$ over $\R$ then it is *absolutely indecomposable* if the representation given by $${M}_a\otimes_\R \overline{\R}: M_i\otimes_\R \overline{\R}\to M_j\otimes_\R \overline{\R}$$ is indecomposable over $\overline{\R}:=\R\otimes_\k \overline{\k},$ where $\overline{\k}$ is the algebraic 