Counting Quiver Representations over Finite Fields Via Graph Enumeration

@article{Helleloid2008CountingQR,
  title={Counting Quiver Representations over Finite Fields Via Graph Enumeration},
  author={Geir T. Helleloid and Fernando Rodriguez Villegas},
  journal={arXiv: Representation Theory},
  year={2008}
}
  • Geir T. Helleloid, Fernando Rodriguez Villegas
  • Published 2008
  • Mathematics
  • arXiv: Representation Theory
  • Let $\Gamma$ be a quiver on n vertices $v_1, v_2, ..., v_n$ with $g_{ij}$ edges between $v_i$ and $v_j$, and let $\alpha \in \N^n$. Hua gave a formula for $A_{\Gamma}(\alpha, q)$, the number of isomorphism classes of absolutely indecomposable representations of $\Gamma$ over the finite field $\F_q$ with dimension vector $\alpha$. Kac showed that $A_{\Gamma}(\bm{\alpha}, q)$ is a polynomial in q with integer coefficients. Using Hua's formula, we show that for each non-negative integer s, the s… CONTINUE READING

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    Counting Quiver Representations over Finite Fields Via Graph Enumeration, submitted, also available at arXiv:0810