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.
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
@article{10_1017_S0017089512000328,
author = {CELIS, ALVARO NOLLA DE},
title = {G-GRAPHS {AND} {SPECIAL} {REPRESENTATIONS} {FOR} {BINARY} {DIHEDRAL} {GROUPS} {IN} {GL(2,C)}},
journal = {Glasgow mathematical journal},
pages = {23--57},
year = {2013},
volume = {55},
number = {1},
doi = {10.1017/S0017089512000328},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000328/}
}
TY - JOUR AU - CELIS, ALVARO NOLLA DE TI - G-GRAPHS AND SPECIAL REPRESENTATIONS FOR BINARY DIHEDRAL GROUPS IN GL(2,C) JO - Glasgow mathematical journal PY - 2013 SP - 23 EP - 57 VL - 55 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000328/ DO - 10.1017/S0017089512000328 ID - 10_1017_S0017089512000328 ER -
%0 Journal Article %A CELIS, ALVARO NOLLA DE %T G-GRAPHS AND SPECIAL REPRESENTATIONS FOR BINARY DIHEDRAL GROUPS IN GL(2,C) %J Glasgow mathematical journal %D 2013 %P 23-57 %V 55 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000328/ %R 10.1017/S0017089512000328 %F 10_1017_S0017089512000328
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