Counting Representations of Valued Quivers over Finite Fields
Keyword(s):
For a symmetrizable Borcherds–Cartan matrix A with integer entries and even diagonal entries, we show that there exists a k-species 𝓢 over the finite field k such that 𝓢 and the Borcherds–Cartan matrix provide the same bilinear form. We also show that the number of isomorphism classes of indecomposable representations of any valued graph with fixed dimension vector is a polynomial, and is independent of the orientation of the valued graph. This extends to the situation of valued graphs with loops.
2017 ◽
Vol 2019
(13)
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pp. 3981-4003
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2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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2012 ◽
Vol 55
(2)
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pp. 418-423
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Keyword(s):
2012 ◽
Vol 23
(09)
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pp. 1250097
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Keyword(s):
2004 ◽
Vol 10
(4)
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pp. 583-614
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2012 ◽
Vol 23
(11)
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pp. 1250116
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2013 ◽
Vol 12
(3)
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pp. 651-676
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2003 ◽
Vol 55
(2)
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pp. 225-246
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