Abstract:
In this paper we present the ongoing research on classifying irreducible representations of the following quiver, or rather the digraph (which throughout this paper we denote by $\mathbb A$):
Every representation of $\mathbb A$ is given by two vector spaces $W_0$ and $W_1$, and two homomorphisms $\varphi_0:W_0\to W_0$ and $\varphi_1:W_1\to W_0$:
We denote the previous representation by $(W_1,W_0,\varphi_1,\varphi_0)$. If $\dim(W_0)=n$ and $\dim(W_1)=m$, we may identify $W_0=K^n$ and $W_1=K^m$, and then $\varphi_0$ and $\varphi_1$ are identified respectively with $n\times n$ and $n\times m$ matrices $M_0$ and $M_1$, so the above representation is determined by the quadruple $(m,n,M_1,M_0)$. We calculate irreducible representations for some $m$.
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