Kavli Affiliate: Yukari Ito
| Summary:
We show a correspondence between the compact exceptional curves and divisors on $G-rm Hilb(mathbfC^3)$ and some non-trivial irreducible representations of $G subset GL(n,C)$ which are special (or essential). Moreover, we provide an explicit construction of the small resolution of $G-rm Hilb(mathbfC^3)$ and, using this resolution, we construct a correspondence between special and essential representations. These results are an extension of “Special McKay correspondence” and “Reid’s recipe”.
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