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- W2023176723 abstract "The geometric McKay correspondence establishes a bijection between the set of nontrivial irreducible representations of a finite subgroup Γ of SL(2, C) and the set of irreducible components of the exceptional divisor in aminimal resolution of the Klein singularity C 2 /Γ. Recently, Y. ITO and I. NAKAMURA found a new interpretation of this fact via a certain Hilbert scheme by which one can construct the minimal resolution in terms of invariant theory of the group Γ. In the case of finite subgroups of GL(2, C) containing no reflections there exists a generalized McKay correspondence if we only consider so-called special representations. Also the Hilbert scheme picture remains true as was conjectured by the author and proven by A. ISHII. In this paper, we demonstrate that the conjecture is - in the case of cyclic quotient singularities - an immediate consequence of an explicit description of the Hilbert scheme given by RIE KIDOH in this journal, and add a proof for some characterizations of special representations and special reflexive sheaves." @default.
- W2023176723 created "2016-06-24" @default.
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- W2023176723 date "2003-02-01" @default.
- W2023176723 modified "2023-10-05" @default.
- W2023176723 title "Special representations and the two-dimensional McKay correspondence" @default.
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- W2023176723 doi "https://doi.org/10.14492/hokmj/1350657526" @default.
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