Geodesic
G-GRAPHS AND SPECIAL REPRESENTATIONS FOR BINARY DIHEDRAL GROUPS IN GL(2,C)
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 23-57

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Given a finite subgroup G⊂GL(2,C), it is known that the minimal resolution of singularity C2/G is the moduli space Y=G-Hilb(C2) of G-clusters ⊂C2. The explicit description of Y can be obtained by calculating every possible distinguished basis for as vector spaces. These basis are the so-called G-graphs. In this paper we classify G-graphs for any small binary dihedral subgroup G in GL(2,C), and in the context of the special McKay correspondence we use this classification to give a combinatorial description of special representations of G appearing in Y in terms of its maximal normal cyclic subgroup H ⊴ G.
DOI : 10.1017/S0017089512000328
Mots-clés : Primary 14E16, Secondary 14C05, 14E15 
CELIS, ALVARO NOLLA DE. G-GRAPHS AND SPECIAL REPRESENTATIONS FOR BINARY DIHEDRAL GROUPS IN GL(2,C). Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 23-57. doi: 10.1017/S0017089512000328
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