Journal Name:
- European Journal of Pure and Applied Mathematics
| Author Name | Faculty of Author |
|---|---|
Abstract (2. Language):
We consider the graph En+1;1 with (n+1) generators 1; :::; n, and , where i has an
edge with i+1 for i = 1; :::; n+1, and 1 has an edge with . We then de ne the Artin group of the
graph En+1;1 for n = 3 and n = 4 and consider its reduced Perron's representation of degrees four
and ve respectively. After we specialize the indeterminates used in de ning the representation
to non-zero complex numbers, we obtain necessary and sucient conditions that guarantee the
irreducibility of the representations for n = 3 and 4 .
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