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15 March 2010 Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds
Jim Bryan, Benjamin Young
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Duke Math. J. 152(1): 115-153 (15 March 2010). DOI: 10.1215/00127094-2010-009

Abstract

We derive two multivariate generating functions for three-dimensional (3D) Young diagrams (also called plane partitions). The variables correspond to a coloring of the boxes according to a finite Abelian subgroup G of SO(3). These generating functions turn out to be orbifold Donaldson-Thomas partition functions for the orbifold [C3/G]. We need only the vertex operator methods of Okounkov, Reshetikhin, and Vafa for the easy case G=Zn; to handle the considerably more difficult case G=Z2×Z2, we also use a refinement of the author's recent q-enumeration of pyramid partitions.

In the appendix, we relate the diagram generating functions to the Donaldson-Thomas partition functions of the orbifold [C3/G]. We find a relationship between the Donaldson-Thomas partition functions of the orbifold and its G-Hilbert scheme resolution. We formulate a crepant resolution conjecture for the Donaldson-Thomas theory of local orbifolds satisfying the hard Lefschetz condition

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Jim Bryan. Benjamin Young. "Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds." Duke Math. J. 152 (1) 115 - 153, 15 March 2010. https://doi.org/10.1215/00127094-2010-009

Information

Published: 15 March 2010
First available in Project Euclid: 11 March 2010

zbMATH: 1230.05019
MathSciNet: MR2643058
Digital Object Identifier: 10.1215/00127094-2010-009

Subjects:
Primary: 05A15
Secondary: 14J32

Rights: Copyright © 2010 Duke University Press

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Vol.152 • No. 1 • 15 March 2010
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